TEST_VALUES
Sample Function Values
TEST_VALUES
is a C++ library which
stores a few selected values of various
mathematical functions.
The intent of TEST_VALUES is to provide a means of making
very simple tests for correctness of software designed to compute
a variety of functions. The testing can be done automatically.
The data provided is generally skimpy, and might not test the
algorithm over a suitably wide range. It does, however, provide
a small amount of reassurance that a given computation is (or
is not) computing the appropriate quantity, and doing so
reasonably accurately.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
TEST_VALUES is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Programs:
CORDIC,
a C++ library which
uses the CORDIC method to compute certain elementary functions.
FN,
a C++ library which
contains routines by Wayne Fullerton for evaluating elementary
and special functions.
GSL,
a C++ library which
includes routines that evaluate many special functions.
LEGENDRE_POLYNOMIAL,
a C++ library which
evaluates the Legendre polynomial and associated functions.
LOBATTO_POLYNOMIAL,
a C++ library which
evaluates Lobatto polynomials, similar to Legendre polynomials
except that they are zero at both endpoints.
POLPAK,
a C++ library which
computes various mathematical functions;
test values for many of these functions are available in
TEST_VALUES.
PROB,
a C++ library which
computes various statistical functions;
test values for many of these functions are available in
TEST_VALUES.
Reference:
-
Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
-
Robert Corless, Gaston Gonnet, David Hare, David Jeffrey,
Donald Knuth,
On the Lambert W Function,
Advances in Computational Mathematics,
Volume 5, 1996, pages 329-359.
-
Gerard Cornuejols, Regina Urbaniak, Robert Weismantel, Laurence Wolsey,
Decomposition of Integer Programs and of Generating Sets,
in Algorithms - ESA '97,
Lecture Notes in Computer Science 1284,
edited by R Burkard, G Woeginger,
Springer, 1997, pages 92-103,
LC: QA76.9.A43.E83.
-
Marc Deleglise, Joel Rivat,
Computing the Summation of the Moebius Function,
Experimental Mathematics,
Volume 5, 1996, pages 291-295.
-
Lester Haar, John Gallagher, George Kell,
NBS/NRC Steam Tables:
Thermodynamic and Transport Properties and Computer Programs
for Vapor and Liquid States of Water in SI Units,
Hemisphere Publishing Corporation, Washington, 1984,
ISBN: 0-89116-353-0,
LC: TJ270.H3.
-
Brian Hayes,
"Why W?",
The American Scientist,
Volume 93, March-April 2005, pages 104-108.
-
Kanti Mardia, Peter Jupp,
Directional Statistics,
Wiley, 2000,
ISBN: 0471953334,
LC: QA276.M335
-
Allan McLeod,
Algorithm 757:
MISCFUN: A software package to compute uncommon
special functions,
ACM Transactions on Mathematical Software,
Volume 22, Number 3, September 1996, pages 288-301.
-
National Bureau of Standards,
Tables of the Bivariate Normal Distribution and Related Functions,
Applied Mathematics Series, Number 50, 1959.
-
Robert Owens,
An Algorithm to Solve the Frobenius Problem,
Mathematics Magazine,
Volume 76, Number 4, October 2003, 264-275.
-
Karl Pearson,
Tables of the Incomplete Beta Function,
Cambridge University Press, 1968,
ISBN: 0521059224,
LC: QA351.P38.
-
Frank Powell,
Statistical Tables for Sociology, Biology and Physical Sciences,
Cambridge University Press, 1982,
ISBN: 0521284732,
LC: QA276.25.S73.
-
Edward Reingold, Nachum Dershowitz,
Calendrical Calculations: The Millennium Edition,
Cambridge University Press, 2001,
ISBN: 0-521-77752-6,
LC: CE12.R45.
-
Johannes van der Corput,
Verteilungsfunktionen,
Proc Akad Amsterdam,
Volume 38, 1935,
Volume 39, 1936.
-
Eric Weisstein,
CRC Concise Encyclopedia of Mathematics,
CRC Press, 2002,
Second edition,
ISBN: 1584883472,
LC: QA5.W45
-
Stephen Wolfram,
The Mathematica Book,
Fourth Edition,
Cambridge University Press, 1999,
ISBN: 0-521-64314-7,
LC: QA76.95.W65.
-
Shanjie Zhang, Jianming Jin,
Computation of Special Functions,
Wiley, 1996,
ISBN: 0-471-11963-6,
LC: QA351.C45.
-
Daniel Zwillinger, editor,
CRC Standard Mathematical Tables and Formulae,
30th Edition,
CRC Press, 1996,
ISBN: 0-8493-2479-3,
LC: QA47.M315.
-
Daniel Zwillinger, Steven Kokoska,
Standard Probability and Statistical Tables,
CRC Press, 2000,
ISBN: 1-58488-059-7,
LC: QA273.3.Z95.
Source Code:
Examples and Tests:
List of Routines:
-
ABRAM0_VALUES returns some values of the Abramowitz0 function.
-
ABRAM1_VALUES returns some values of the Abramowitz1 function.
-
ABRAM2_VALUES returns some values of the Abramowitz2 function.
-
AGM_VALUES returns some values of the AGM.
-
AIRY_AI_VALUES returns some values of the Airy Ai(x) function.
-
AIRY_AI_INT_VALUES returns some values of the integral of the Airy function.
-
AIRY_AI_PRIME_VALUES returns some values of the Airy function Ai'(x).
-
AIRY_BI_VALUES returns some values of the Airy Bi(x) function.
-
AIRY_BI_INT_VALUES returns some values of the integral of the Airy function.
-
AIRY_BI_PRIME_VALUES returns some values of the Airy function Bi'(x).
-
AIRY_CAI_VALUES returns some values of the Airy Ai(x) for complex argument.
-
AIRY_CBI_VALUES returns some values of the Airy Bi(x) for complex argument.
-
AIRY_GI_VALUES returns some values of the Airy Gi function.
-
AIRY_HI_VALUES returns some values of the Airy Hi function.
-
ARCCOS_VALUES returns some values of the arc cosine function.
-
ARCCOSH_VALUES returns some values of the hyperbolic arc cosine function.
-
ARCSIN_VALUES returns some values of the arc sine function.
-
ARCSINH_VALUES returns some values of the hyperbolic arc sine function.
-
ARCTAN_VALUES returns some values of the arc tangent function.
-
ARCTAN_INT_VALUES returns some values of the inverse tangent integral.
-
ARCTAN2_VALUES: arc tangent function of two arguments.
-
ARCTANH_VALUES returns some values of the hyperbolic arc tangent function.
-
BEI0_VALUES returns some values of the Kelvin BEI function of order NU = 0.
-
BEI1_VALUES returns some values of the Kelvin BEI function of order NU = 1.
-
BELL_VALUES returns some values of the Bell numbers.
-
BER0_VALUES returns some values of the Kelvin BER function of order NU = 0.
-
BER1_VALUES returns some values of the Kelvin BER function of order NU = 1.
-
BERNOULLI_NUMBER_VALUES returns some values of the Bernoulli numbers.
-
BERNOULLI_POLY_VALUES returns some values of the Bernoulli polynomials.
-
BERNSTEIN_POLY_01_VALUES returns some values of the Bernstein polynomials.
-
BESSEL_I0_INT_VALUES returns some values of the Bessel I0 integral.
-
BESSEL_I0_SPHERICAL_VALUES returns some values of the Spherical Bessel function i0.
-
BESSEL_I0_VALUES returns some values of the I0 Bessel function.
-
BESSEL_I1_SPHERICAL_VALUES returns some values of the Spherical Bessel function i1.
-
BESSEL_I1_VALUES returns some values of the I1 Bessel function.
-
BESSEL_IN_VALUES returns some values of the In Bessel function.
-
BESSEL_IX_VALUES returns some values of the Ix Bessel function.
-
BESSEL_J_SPHERICAL_VALUES returns values of the Spherical Bessel function j.
-
BESSEL_J0_INT_VALUES returns some values of the Bessel J0 integral.
-
BESSEL_J0_SPHERICAL_VALUES returns some values of the Spherical Bessel function j0.
-
BESSEL_J0_ZERO_VALUES returns some values of zeroes of the J0 Bessel function.
-
BESSEL_J0_VALUES returns some values of the J0 Bessel function.
-
BESSEL_J1_SPHERICAL_VALUES returns some values of the Spherical Bessel function j1.
-
BESSEL_J1_VALUES returns some values of the J1 Bessel function.
-
BESSEL_JN_VALUES returns some values of the Jn Bessel function.
-
BESSEL_JX_VALUES returns some values of the Jx Bessel function.
-
BESSEL_K0_VALUES returns some values of the K0 Bessel function.
-
BESSEL_K0_INT_VALUES returns some values of the Bessel K0 integral.
-
BESSEL_K1_VALUES returns some values of the K1 Bessel function.
-
BESSEL_KN_VALUES returns some values of the Kn Bessel function.
-
BESSEL_KX_VALUES returns some values of the Kx Bessel function.
-
BESSEL_Y0_VALUES returns some values of the Y0 Bessel function.
-
BESSEL_Y0_INT_VALUES returns some values of the Bessel Y0 integral.
-
BESSEL_Y0_SPHERICAL_VALUES returns some values of the Spherical Bessel function y0.
-
BESSEL_Y1_VALUES returns some values of the Y1 Bessel function.
-
BESSEL_Y1_SPHERICAL_VALUES returns some values of the Spherical Bessel function y1.
-
BESSEL_YN_VALUES returns some values of the Yn Bessel function.
-
BESSEL_YX_VALUES returns some values of the Yx Bessel function.
-
BETA_CDF_VALUES returns some values of the Beta CDF.
-
BETA_INC_VALUES returns some values of the incomplete Beta function.
-
BETA_LOG_VALUES returns some values of the logarithm of the Beta function.
-
BETA_NONCENTRAL_CDF_VALUES returns some values of the noncentral Beta CDF.
-
BETA_PDF_VALUES returns some values of the Beta PDF.
-
BETA_VALUES returns some values of the Beta function.
-
BINOMIAL_VALUES returns some values of the binomial coefficients.
-
BINOMIAL_CDF_VALUES returns some values of the binomial CDF.
-
BINOMIAL_PDF_VALUES returns some values of the binomial PDF.
-
BIVARIATE_NORMAL_CDF_VALUES returns some values of the bivariate normal CDF.
-
CATALAN_VALUES returns some values of the Catalan numbers.
-
CAUCHY_CDF_VALUES returns some values of the Cauchy CDF.
-
CBRT_VALUES returns some values of the cube root function.
-
CHEBY_T_POLY_VALUES returns values of Chebyshev polynomials T(n,x).
-
CHEBY_T01_POLY_VALUES: values of shifted Chebyshev polynomials T01(n,x).
-
CHEBY_U_POLY_VALUES returns values of Chebyshev polynomials U(n,x).
-
CHEBY_U01_POLY_VALUES: values of shifted Chebyshev polynomials U01(n,x).
-
CHEBY_V_POLY_VALUES returns values of Chebyshev polynomials V(n,x).
-
CHEBY_V01_POLY_VALUES: values of shifted Chebyshev polynomials V01(n,x).
-
CHEBY_W_POLY_VALUES returns values of Chebyshev polynomials W(n,x).
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CHEBY_W01_POLY_VALUES: values of shifted Chebyshev polynomials W01(n,x).
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CHI_VALUES returns some values of the hyperbolic cosine integral function.
-
CHI_SQUARE_CDF_VALUES returns some values of the Chi-Square CDF.
-
CHI_SQUARE_PDF_VALUES returns some values of the Chi-Square PDF.
-
CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral chi CDF.
-
CI_VALUES returns some values of the cosine integral function.
-
CIN_VALUES returns some values of the alternate cosine integral function.
-
CINH_VALUES returns some values of the alternate hyperbolic cosine integral.
-
CLAUSEN_VALUES returns some values of the Clausen's integral.
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CLEBSCH_GORDAN_VALUES returns some values of the Clebsch-Gordan function.
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COLLATZ_COUNT_VALUES returns some values of the Collatz count function.
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COS_VALUES returns some values of the cosine function.
-
COS_DEGREE_VALUES: values of the cosine function for degree arguments.
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COS_POWER_INT_VALUES returns some values of the sine power integral.
-
COSH_VALUES returns some values of the hyperbolic cosine function.
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COT_VALUES returns some values of the cotangent function.
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CP_VALUES returns some values of the specific heat at constant pressure.
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DATENUM_VALUES returns the MATLAB datenum for various dates.
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DAWSON_VALUES returns some values of Dawson's integral.
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DEBYE1_VALUES returns some values of Debye's function of order 1.
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DEBYE2_VALUES returns some values of Debye's function of order 2.
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DEBYE3_VALUES returns some values of Debye's function of order 3.
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DEBYE4_VALUES returns some values of Debye's function of order 4.
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DIELECTRIC_VALUES returns some values of the static dielectric constant.
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DEDEKIND_SUM_VALUES returns some values of the Dedekind sum.
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DILOGARITHM_VALUES returns some values of the dilogarithm function.
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E1_VALUES returns some values of the exponential integral function E1(X).
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EASTER_GREGORIAN_VALUES: dates of Easter in Gregorian calendar.
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EASTER_JULIAN_VALUES: dates of Easter in Julian calendar.
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EI_VALUES returns some values of the exponential integral function EI(X).
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ELLIPTIC_EA_VALUES returns values of the complete elliptic integral E(A).
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ELLIPTIC_EK_VALUES returns values of the complete elliptic integral E(K).
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ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
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ELLIPTIC_FA_VALUES returns values of the complete elliptic integral F(A).
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ELLIPTIC_FK_VALUES returns values of the complete elliptic integral F(K).
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ELLIPTIC_FM_VALUES returns values of the complete elliptic integral F(M).
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ELLIPTIC_INC_EA_VALUES: values of the incomplete elliptic integral E(PHI,A).
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ELLIPTIC_INC_EK_VALUES: values of the incomplete elliptic integral E(PHI,K).
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ELLIPTIC_INC_EM_VALUES: values of the incomplete elliptic integral E(PHI,M).
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ELLIPTIC_INC_FA_VALUES: values of the incomplete elliptic integral F(PHI,A).
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ELLIPTIC_INC_FK_VALUES: values of the incomplete elliptic integral F(PHI,K).
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ELLIPTIC_INC_FM_VALUES: values of the incomplete elliptic integral F(PHI,M).
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ELLIPTIC_INC_PIA_VALUES: values of incomplete elliptic integral Pi(PHI,N,A).
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ELLIPTIC_INC_PIK_VALUES: values of incomplete elliptic integral Pi(PHI,N,K).
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ELLIPTIC_INC_PIM_VALUES: values of incomplete elliptic integral Pi(PHI,N,M).
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ELLIPTIC_PIA_VALUES returns values of the complete elliptic integral Pi(A).
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ELLIPTIC_PIK_VALUES returns values of the complete elliptic integral Pi(K).
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ELLIPTIC_PIM_VALUES returns values of the complete elliptic integral Pi(M).
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ERF_VALUES returns some values of the ERF or "error" function.
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ERFC_VALUES returns some values of the ERFC or "complementary error" function.
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EULER_NUMBER_VALUES returns some values of the Euler numbers.
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EULER_POLY_VALUES returns some values of the Euler polynomials.
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EXP_VALUES returns some values of the exponential function.
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EXP3_INT_VALUES returns some values of the EXP3 integral function.
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EXPONENTIAL_01_PDF_VALUES returns some values of the standard exponential PDF.
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EXPONENTIAL_CDF_VALUES returns some values of the Exponential CDF.
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EXPONENTIAL_PDF_VALUES returns some values of the Exponential PDF.
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EXTREME_VALUES_CDF_VALUES returns some values of the Extreme Values CDF.
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F_CDF_VALUES returns some values of the F CDF test function.
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F_NONCENTRAL_CDF_VALUES returns some values of the F CDF test function.
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FRESNEL_COS_VALUES returns values of the Fresnel cosine integral function.
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FRESNEL_SIN_VALUES returns some values of the Fresnel sine integral function.
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FROBENIUS_NUMBER_DATA_VALUES returns data for the Frobenius problem.
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FROBENIUS_NUMBER_ORDER_VALUES returns orders of the Frobenius problem.
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FROBENIUS_NUMBER_ORDER2_VALUES returns values of the order 2 Frobenius number.
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GAMMA_VALUES returns some values of the Gamma function.
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GAMMA_01_PDF_VALUES returns some values of the standard Gamma PDF.
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GAMMA_CDF_VALUES returns some values of the Gamma CDF.
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GAMMA_INC_P_VALUES: values of normalized incomplete Gamma function P(A,X).
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GAMMA_INC_Q_VALUES: values of normalized incomplete Gamma function Q(A,X).
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GAMMA_INC_TRICOMI_VALUES: values of Tricomi's incomplete Gamma function.
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GAMMA_INC_VALUES returns some values of the incomplete Gamma function.
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GAMMA_LOG_VALUES returns some values of the Log Gamma function.
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GAMMA_PDF_VALUES returns some values of a Gamma PDF.
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GEGENBAUER_POLY_VALUES returns some values of the Gegenbauer polynomials.
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GEOMETRIC_CDF_VALUES returns values of the geometric CDF.
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GOODWIN_VALUES returns some values of the Goodwin and Staton function.
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GUD_VALUES returns some values of the Gudermannian function.
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HERMITE_FUNCTION_VALUES returns some values of the Hermite function.
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HERMITE_POLY_PHYS_VALUES returns some values of the physicist's Hermite polynomial.
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HERMITE_POLY_PROB_VALUES: values of the probabilist's Hermite polynomial.
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HYPER_1F1_VALUES returns some values of the hypergeometric function 1F1.
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HYPER_2F1_VALUES returns some values of the hypergeometric function 2F1.
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HYPERGEOMETRIC_CDF_VALUES returns some values of the hypergeometric CDF.
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HYPERGEOMETRIC_PDF_VALUES returns some values of the hypergeometric PDF.
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HYPERGEOMETRIC_U_VALUES: some values of the hypergeometric function U(a,b,x).
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I0ML0_VALUES returns some values of the I0ML0 function.
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I1ML1_VALUES returns some values of the I1ML1 function.
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I4_FACTORIAL_VALUES returns values of the factorial function.
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I4_FACTORIAL2_VALUES returns values of the double factorial function.
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I4_FALL_VALUES returns values of the integer falling factorial function.
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I4_RISE_VALUES returns values of the integer rising factorial function.
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INT_VALUES returns some values of the "integer part" function.
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INVERSE_CHI_SQUARE_PDF_VALUES returns values of the inverse Chi-Square PDF.
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INVERSE_GAMMA_PDF_VALUES returns values of the inverse Gamma PDF.
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JACOBI_CN_VALUES returns some values of the Jacobi elliptic function CN(A,X).
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JACOBI_DN_VALUES returns some values of the Jacobi elliptic function DN(A,X).
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JACOBI_POLY_VALUES returns some values of the Jacobi polynomial.
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JACOBI_SN_VALUES returns some values of the Jacobi elliptic function SN(A,X).
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JED_CE_VALUES returns the Common Era dates for Julian Ephemeris Dates.
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JED_MJD_VALUES returns the MJD for Julian Ephemeris Dates.
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JED_RD_VALUES returns the RD for Julian Ephemeris Dates.
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JED_WEEKDAY_VALUES returns the day of the week for Julian Ephemeris Dates.
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KEI0_VALUES returns some values of the Kelvin KEI function of order NU = 0.
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KEI1_VALUES returns some values of the Kelvin KEI function of order NU = 1.
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KER0_VALUES returns some values of the Kelvin KER function of order NU = 0.
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KER1_VALUES returns some values of the Kelvin KER function of order NU = 1.
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LAGUERRE_ASSOCIATED_VALUES returns some values of the associated Laguerre polynomials.
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LAGUERRE_GENERAL_VALUES returns some values of the generalized Laguerre function.
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LAGUERRE_POLYNOMIAL_VALUES returns some values of the Laguerre polynomial.
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LAMBERT_W_VALUES returns some values of the Lambert W function.
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LAPLACE_CDF_VALUES returns some values of the Laplace CDF.
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LEGENDRE_ASSOCIATED_VALUES returns values of associated Legendre functions.
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LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES: normalized associated Legendre.
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LEGENDRE_ASSOCIATED_NORMALIZED_VALUES: normalized associated Legendre.
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LEGENDRE_FUNCTION_Q_VALUES returns values of the Legendre Q function.
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LEGENDRE_NORMALIZED_POLYNOMIAL_VALUES: the normalized Legendre polynomials.
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LEGENDRE_POLYNOMIAL_VALUES returns values of the Legendre polynomials.
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LEGENDRE_SHIFTED_POLYNOMIAL_VALUES: values of shifted Legendre polynomials.
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LOBATTO_POLYNOMIAL_VALUES returns values of the completed Lobatto polynomials.
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LOBATTO_POLYNOMIAL_DERIVATIVES: derivatives of the completed Lobatto polynomials.
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LERCH_VALUES returns some values of the Lerch transcendent function.
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LINEAR_SYSTEM_VALUES returns some linear systems.
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LOBACHEVSKY_VALUES returns some values of the Lobachevsky function.
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LOG_VALUES returns some values of the natural logarithm function.
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LOG_NORMAL_CDF_VALUES returns some values of the Log Normal CDF.
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LOG_SERIES_CDF_VALUES returns some values of the log series CDF.
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LOG10_VALUES returns some values of the logarithm base 10 function.
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LOGARITHMIC_INTEGRAL_VALUES returns values of the logarithmic integral LI(X).
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LOGISTIC_CDF_VALUES returns some values of the Logistic CDF.
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MERTENS_VALUES returns some values of the Mertens function.
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MITTAG_LEFFLER_EA_VALUES: values of one-parameter Mittag Leffler function.
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MITTAG_LEFFLER_EAB_VALUES: values of two-parameter Mittag Leffler function.
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MOEBIUS_VALUES returns some values of the Moebius function.
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MULTINOMIAL_PDF_SIZES returns sizes of some multinomial PDF data.
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MULTINOMIAL_PDF_VALUES returns some values of the multinomial PDF.
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NEGATIVE_BINOMIAL_CDF_VALUES returns values of the negative binomial CDF.
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NINE_J_VALUES returns some values of the Wigner 9J function.
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NORMAL_01_CDF_VALUES returns some values of the Normal 01 CDF.
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NORMAL_01_PDF_VALUES returns some values of the Normal 01 PDF.
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NORMAL_CDF_VALUES returns some values of the Normal CDF.
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NORMAL_PDF_VALUES returns some values of the Normal PDF.
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OMEGA_VALUES returns some values of the OMEGA function.
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OWEN_VALUES returns some values of Owen's T function.
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PARTITION_COUNT_VALUES returns some values of the int *partition count.
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PARTITION_DISTINCT_COUNT_VALUES returns some values of Q(N).
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PHI_VALUES returns some values of the PHI function.
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PI_VALUES returns values of the Pi function.
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POISSON_CDF_VALUES returns some values of the Poisson CDF.
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POLYLOGARITHM_VALUES returns some values of the polylogarithm.
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POLYOMINO_CHIRAL_COUNT_VALUES counts chiral polyominoes (allowing holes).
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POLYOMINO_FIXED_COUNT_VALUES counts fixed polyominoes (allowing holes).
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POLYOMINO_FREE_COUNT_VALUES counts free polyominoes (allowing holes).
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PRANDTL_VALUES returns some values of the Prandtl number.
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PRIME_VALUES returns values of the prime function.
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PSAT_VALUES returns some values of the saturation pressure.
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PSI_VALUES returns some values of the Psi or Digamma function.
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R8_FACTORIAL_VALUES returns values of the real factorial function.
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R8_FACTORIAL_LOG_VALUES returns values of log(n!).
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R8_FACTORIAL2_VALUES returns values of the double factorial function.
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R8_FALL_VALUES returns some values of the falling factorial function.
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R8_RISE_VALUES returns some values of the rising factorial function.
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RAYLEIGH_CDF_VALUES returns some values of the Rayleigh CDF.
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SCALED_INVERSE_CHI_SQUARE_PDF_VALUES: scaled inverse Chi-Square PDF values.
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SECVIR_VALUES returns some values of the second virial coefficient.
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SHI_VALUES returns some values of the hyperbolic sine integral function.
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SI_VALUES returns some values of the sine integral function.
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SIGMA_VALUES returns some values of the Sigma function.
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SIN_VALUES returns some values of the sine function.
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SIN_DEGREE_VALUES: the sine function with argument in degrees.
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SIN_POWER_INT_VALUES returns some values of the sine power integral.
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SINH_VALUES returns some values of the hyperbolic sine function.
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SIX_J_VALUES returns some values of the Wigner 6J function.
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SOUND_VALUES returns some values of the speed of sound.
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SPHERE_UNIT_AREA_VALUES returns some areas of the unit sphere in ND.
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SPHERE_UNIT_VOLUME_VALUES returns some volumes of the unit sphere in ND.
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SPHERICAL_HARMONIC_VALUES returns values of spherical harmonic functions.
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SQRT_VALUES returns some values of the square root function.
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STIRLING1_VALUES returns some values of the Stirling numbers, kind 1.
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STIRLING2_VALUES returns some values of the Stirling numbers, kind 2.
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STROMGEN_VALUES returns some values of the Stromgen function.
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STRUVE_H0_VALUES returns some values of the Struve H0 function.
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STRUVE_H1_VALUES returns some values of the Struve H1 function.
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STRUVE_L0_VALUES returns some values of the Struve L0 function.
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STRUVE_L1_VALUES returns some values of the Struve L1 function.
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STUDENT_CDF_VALUES returns some values of the Student CDF.
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STUDENT_NONCENTRAL_CDF_VALUES returns values of the noncentral Student CDF.
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SUBFACTORIAL_VALUES returns values of the subfactorial function.
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SURTEN_VALUES returns some values of the surface tension.
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SYNCH1_VALUES returns some values of the synchrotron radiation function.
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SYNCH2_VALUES returns some values of the synchrotron radiation function.
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TAN_VALUES returns some values of the tangent function.
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TANH_VALUES returns some values of the hyperbolic tangent function.
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TAU_VALUES returns some values of the Tau function.
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THERCON_VALUES returns some values of the thermal conductivity.
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THREE_J_VALUES returns some values of the Wigner 3J function.
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TIMESTAMP prints the current YMDHMS date as a time stamp.
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TRAN02_VALUES returns some values of the order 2 transportation function.
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TRAN03_VALUES returns some values of the order 3 transportation function.
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TRAN04_VALUES returns some values of the order 4 transportation function.
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TRAN05_VALUES returns some values of the order 5 transportation function.
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TRAN06_VALUES returns some values of the order 6 transportation function.
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TRAN07_VALUES returns some values of the order 7 transportation function.
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TRAN08_VALUES returns some values of the order 8 transportation function.
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TRAN09_VALUES returns some values of the order 9 transportation function.
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TRIGAMMA_VALUES returns some values of the TriGamma function.
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TRUNCATED_NORMAL_AB_CDF_VALUES: values of the Truncated Normal CDF.
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TRUNCATED_NORMAL_AB_PDF_VALUES: values of the Truncated Normal PDF.
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TRUNCATED_NORMAL_A_CDF_VALUES: values of the Lower Truncated Normal CDF.
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TRUNCATED_NORMAL_A_PDF_VALUES: values of the Lower Truncated Normal PDF.
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TRUNCATED_NORMAL_B_CDF_VALUES: values of the upper Truncated Normal CDF.
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TRUNCATED_NORMAL_B_PDF_VALUES: values of the Upper Truncated Normal PDF.
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TSAT_VALUES returns some values of the saturation temperature.
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VAN_DER_CORPUT_VALUES returns some values of the van der Corput sequence.
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VISCOSITY_VALUES returns some values of the viscosity function.
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VON_MISES_CDF_VALUES returns some values of the von Mises CDF.
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WEEKDAY_VALUES returns the day of the week for various dates.
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WEIBULL_CDF_VALUES returns some values of the Weibull CDF.
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WRIGHT_OMEGA_VALUES returns some values of the Wright Omega function.
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ZETA_VALUES returns some values of the Riemann Zeta function.
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ZETA_M1_VALUES returns some values of the Riemann Zeta Minus One function.
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the C++ source codes.
Last revised on 24 June 2018.