TOMS757
Uncommon Special Functions

TOMS757 is a FORTRAN77 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 FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

TEST_VALUES, a FORTRAN77 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.f, the source code;
• toms757.sh, commands to compile the source code;

Examples and Tests:

• toms757_prb.f, the sample test code;
• toms757_prb.sh, commands to compile the test code;
• toms757_prb_output.txt, output from a run of the test code;

List of Routines:

• ABRAM0 evaluates the Abramowitz function of order 0.
• ABRAM1 evaluates the Abramowitz function of order 1.
• ABRAM2 evaluates the Abramowitz function of order 2.
• AIRINT calculates the integral of the Airy function Ai.
• AIRYGI computes the modified Airy function Gi(x).
• AIRYHI computes the modified Airy function Hi(x).
• ATNINT calculates the inverse tangent integral.
• BIRINT calculates the integral of the Airy function Bi.
• CLAUSN calculates Clausen's integral.
• DEBYE1 calculates the Debye function of order 1.
• DEBYE2 calculates the Debye function of order 2.
• DEBYE3 calculates the Debye function of order 3.
• DEBYE4 calculates the Debye function of order 4.
• EXP3 calculates the integral of exp(-t^3).
• GOODST calculates the integral of exp(-t^2/(t+x)).
• I0INT computes the integral of the modified Bessel function I0(X).
• I0ML0 calculates the difference between the Bessel I0 and Struve L0 functions.
• I1ML1 calculates the difference between the Bessel I1 and Struve L1 functions.
• J0INT calculates the integral of the Bessel function J0.
• K0INT calculates the integral of the modified Bessel function K0(X).
• LOBACH calculates the Lobachevsky function.
• STROM calculates Stromgen's integral.
• STRVH0 calculates the Struve function of order 0.
• STRVH1 calculates the Struve function of order 1.
• STRVL0 calculates the modified Struve function of order 0.
• STRVL1 calculates the modified Struve function of order 1.
• SYNCH1 calculates the synchrotron radiation function.
• SYNCH2 calculates the synchrotron radiation function.
• TRAN02 calculates the transport integral of order 2.
• TRAN03 calculates the transport integral of order 3.
• TRAN04 calculates the transport integral of order 4.
• TRAN05 calculates the transport integral of order 5.
• TRAN06 calculates the transport integral of order 6.
• TRAN07 calculates the transport integral of order 7.
• TRAN08 calculates the transport integral of order 8.
• TRAN09 calculates the transport integral of order 9.
• BESSEL_Y0_INT calculates the integral of the Bessel function Y0.
• CHEVAL evaluates a Chebyshev series.
• ERRPRN prints an error message.

You can go up one level to the FORTRAN770 source codes.