TOMS715
Special Functions

TOMS715 is a FORTRAN77 library which evaluates special functions, including the Bessel I, J, K, and Y functions of order 0, of order 1, and of any real order, Dawson's integral, the error function, exponential integrals, the gamma function, the normal distribution function, the psi function. This is a version of ACM TOMS algorithm 715.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

TOMS715 is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

FN, a FORTRAN77 library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y, beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals include hyperbolic cosine, cosine, Dawson, exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.

SPECFUN, a FORTRAN77 library which computes special functions, including Bessel I, J, K and Y functions, and the Dawson, E1, EI, Erf, Gamma, log Gamma, Psi/Digamma functions, by William Cody and Laura Stoltz;

SPECIAL_FUNCTIONS, a FORTRAN77 library which computes the Beta, Error, Gamma, Lambda, Psi functions, the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, the Bernoulli and Euler numbers, the Hermite, Laguerre and Legendre polynomials, the cosine, elliptic, exponential, Fresnel and sine integrals, by Shanjie Zhang, Jianming Jin;

TOMS511, a FORTRAN77 library which can evaluate Bessel I or J functions of real (non integer) order, This is a version of ACM TOMS Algorithm 515;

TOMS597, a FORTRAN77 library which can evaluate Bessel I functions of real (non integer) order, This is a version of ACM TOMS Algorithm 597;

TOMS644, a FORTRAN77 library which evaluates the Bessel I, J, K, Y functions, the Airy functions Ai and Bi, and the Hankel function, for complex argument and real order. This is a version of ACM TOMS algorithm 644.

Reference:

1. William Cody,
   Algorithm 715: SPECFUN - A Portable FORTRAN Package of Special Function Routines and Test Drivers,
   ACM Transactions on Mathematical Software,
   Volume 19, Number 1, March 1993, pages 22-32.

Source Code:

• toms715.f, the source code.

Examples and Tests:

• toms715_prb.f, a sample calling program.
• toms715_prb_output.txt, the output file.

List of Routines:

• ANORM evaluates the normal distribution function.
• BESEI0 evaluates the exponentially scaled Bessel I function of order 0.
• BESEI1 evaluates the exponentially scaled Bessel I function of order 1.
• BESEK0 evaluates the exponentially scaled Bessel K function of order 0.
• BESEK1 evaluates the exponentially scaled Bessel K function of order 1.
• BESI0 evaluates the modified Bessel I function of order 0.
• BESI1 evaluates the modified Bessel I function of order 1.
• BESJ0 evaluates the Bessel J function of order 0.
• BESJ1 evaluates the Bessel J function of order 1.
• BESK0 evaluates the modified Bessel K function of order 0.
• BESK1 evaluates the modified Bessel K function of order 1.
• BESY0 evaluates the Bessel Y function of order 0.
• BESY1 evaluates the Bessel Y function of order 1.
• CALCEI computes exponential integrals.
• CALCI0 evaluates modified Bessel I functions of order 0.
• CALCI1 evaluates modified Bessel I functions of order 1.
• CALCK0 evaluates modified Bessel K functions of order 0.
• CALCK1 evaluates modifies Bessel K functions of order 1.
• CALJY0 evaluates Bessel J and Y functions of order 0.
• CALJY1 evaluates Bessel J and Y functions of order 1.
• CALERF evaluates the error function and related quantities.
• DAW evaluates Dawson's integral
• DLGAMA calculates the logarithm of the gamma function.
• DSUBN evaluates derivatives of Ei(X).
• EI evaluates the exponential integral Ei(x).
• EONE evaluates the exponential integral E1(x).
• DERF evaluates the error function.
• DERFC evaluates the complementary error function.
• DERFCX evaluates exp(x^2) * erfc(x).
• EXPEI evaluates exp(-x) * Ei(x).
• DGAMMA evaluates the gamma function.
• MACHAR determines the machine arithmetic parameters.
• PSI evaluates the Psi function.
• REN is a random number generator.
• RIBESL evaluates a sequence of Bessel I functions.
• RJBESL evaluates a sequence of Bessel J functions.
• RKBESL evaluates a sequence of Bessel K functions.
• RYBESL evaluates a sequence of Bessel Y functions.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.