TOMS757
Uncommon Special Functions

TOMS757 is a FORTRAN90 library which evaluates a number of uncommon special functions, by Allan McLeod.

TOMS757 is a FORTRAN90 version of ACM TOMS algorithm 757.

The special functions include:

• the Abramowitz function of several orders;
• integrals of the Airy functions Ai(x) and Bi(x);
• Clausen's integral;
• Debye integrals of several orders;
• integrals of the Bessel functions I0, J0, K0 and Y0;
• Struve functions;
• the synchrotron radiation integral;
• the transport integral of several orders;

The original, true, correct version of ACM TOMS Algorithm 757 is available through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html

The version displayed here has been converted to FORTRAN90, and other internal changes have been made to suit me.

Languages:

TOMS757 is available in a FORTRAN90 version.

Related Data and Programs:

TEST_VALUES, a FORTRAN90 library which contains routines which store selected values of various special functions.

Author:

Allan McLeod,
Department of Mathematics and Statistics,
Paisley University, Scotland.

Reference:

1. 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.

Source Code:

• toms757.f90, the source code;

Examples and Tests:

• toms757_test.f90, the sample test code;
• toms757_test.txt, output from a run of the test code;

List of Routines:

• ABRAM0 evaluates the Abramowitz function of order 0.
• ABRAM0_VALUES returns some values of the Abramowitz0 function.
• ABRAM1 evaluates the Abramowitz function of order 1.
• ABRAM1_VALUES returns some values of the Abramowitz1 function.
• ABRAM2 evaluates the Abramowitz function of order 2.
• ABRAM2_VALUES returns some values of the Abramowitz2 function.
• AIRY_AI_INT calculates the integral of the Airy function Ai.
• AIRY_AI_INT_VALUES returns some values of the integral of the Airy function.
• AIRY_BI_INT calculates the integral of the Airy function Bi.
• AIRY_BI_INT_VALUES returns some values of the integral of the Airy function.
• AIRY_GI computes the modified Airy function Gi(x).
• AIRY_GI_VALUES returns some values of the Airy Gi function.
• AIRY_HI computes the modified Airy function Hi(x).
• AIRY_HI_VALUES returns some values of the Airy Hi function.
• ARCTAN_INT calculates the inverse tangent integral.
• ARCTAN_INT_VALUES returns some values of the inverse tangent integral.
• BESSEL_I0_INT computes the integral of the modified Bessel function I0(X).
• BESSEL_I0_INT_VALUES returns some values of the Bessel I0 integral.
• BESSEL_J0_INT calculates the integral of the Bessel function J0.
• BESSEL_J0_INT_VALUES returns some values of the Bessel J0 integral.
• BESSEL_K0_INT calculates the integral of the modified Bessel function K0(X).
• BESSEL_K0_INT_VALUES returns some values of the Bessel K0 integral.
• BESSEL_Y0_INT calculates the integral of the Bessel function Y0.
• BESSEL_Y0_INT_VALUES returns some values of the Bessel Y0 integral.
• CHEVAL evaluates a Chebyshev series.
• CLAUSEN calculates Clausen's integral.
• CLAUSEN_VALUES returns some values of the Clausen's integral.
• DEBYE1 calculates the Debye function of order 1.
• DEBYE1_VALUES returns some values of Debye's function of order 1.
• DEBYE2 calculates the Debye function of order 2.
• DEBYE2_VALUES returns some values of Debye's function of order 2.
• DEBYE3 calculates the Debye function of order 3.
• DEBYE3_VALUES returns some values of Debye's function of order 3.
• DEBYE4 calculates the Debye function of order 4.
• DEBYE4_VALUES returns some values of Debye's function of order 4.
• EXP3_INT calculates the integral of exp(-t^3).
• EXP3_INT_VALUES returns some values of the EXP3 integral function.
• GOODWIN calculates the integral of exp(-t^2/(t+x)).
• GOODWIN_VALUES returns some values of the Goodwin and Staton function.
• I0ML0 calculates the difference between the Bessel I0 and Struve L0 functions.
• I0ML0_VALUES returns some values of the I0ML0 function.
• I1ML1 calculates the difference between the Bessel I1 and Struve L1 functions.
• I1ML1_VALUES returns some values of the I1ML1 function.
• LOBACHEVSKY calculates the Lobachevsky function.
• LOBACHEVSKY_VALUES returns some values of the Lobachevsky function.
• STROMGEN calculates Stromgen's integral.
• STROMGEN_VALUES returns some values of the Stromgen function.
• STRUVE_H0 calculates the Struve function of order 0.
• STRUVE_H0_VALUES returns some values of the Struve H0 function.
• STRUVE_H1 calculates the Struve function of order 1.
• STRUVE_H1_VALUES returns some values of the Struve H1 function.
• STRUVE_L0 calculates the modified Struve function of order 0.
• STRUVE_L0_VALUES returns some values of the Struve L0 function.
• STRUVE_L1 calculates the modified Struve function of order 1.
• STRUVE_L1_VALUES returns some values of the Struve L1 function.
• SYNCH1 calculates the synchrotron radiation function.
• SYNCH1_VALUES returns some values of the synchrotron radiation function.
• SYNCH2 calculates the synchrotron radiation function.
• SYNCH2_VALUES returns some values of the synchrotron radiation function.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.
• TRAN02 calculates the transport integral of order 2.
• TRAN02_VALUES returns some values of the order 2 transportation function.
• TRAN03 calculates the transport integral of order 3.
• TRAN03_VALUES returns some values of the order 3 transportation function.
• TRAN04 calculates the transport integral of order 4.
• TRAN04_VALUES returns some values of the order 4 transportation function.
• TRAN05 calculates the transport integral of order 5.
• TRAN05_VALUES returns some values of the order 5 transportation function.
• TRAN06 calculates the transport integral of order 6.
• TRAN06_VALUES returns some values of the order 6 transportation function.
• TRAN07 calculates the transport integral of order 7.
• TRAN07_VALUES returns some values of the order 7 transportation function.
• TRAN08 calculates the transport integral of order 8.
• TRAN08_VALUES returns some values of the order 8 transportation function.
• TRAN09 calculates the transport integral of order 9.
• TRAN09_VALUES returns some values of the order 9 transportation function.

You can go up one level to the FORTRAN90 source codes.