B300: An integral of type

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 15.03.1993
Language: Fortran	Revised:

Subroutine subprograms RSRTNT and DSRTNT calculate, based on indefinite integration, the definite integral

for k=-3,-2,-1,0,1,2,3 and n=1,3, provided that for u < x < v and the limits u,v are such that the integral converges. In particular, the Cauchy principal value is taken if k=-1 and uv < 0.

On CDC and Cray computers, the double-precision version DSRTNT is not provided.

Structure:

SUBROUTINE subprograms
User Entry Names : RSRTNT, DSRTNT
Files Referenced : Unit 6
External References: MTLMTR, ABEND

Usage:

For (type REAL), (type DOUBLE PRECISION),

    CALL tSRTNT(K,N,A,B,C,U,V,RES,LRL)

K

(INTEGER) Power k of x.

N

(INTEGER) Power n of .

A,B,C

(type according to t) Coefficients a,b,c.

U,V

(type according to t) Limits of integration u,v.

RES

(type according to t) Contains, on exit, the value I provided , the value zero otherwise.

LRL

(LOGICAL) Contains, on exit, the value .TRUE. if the integral exists in the sense described above, the value .FALSE. otherwise.

Restrictions:

1. 2. ; or .

Error handling:

Error B300.1: Restriction 1 is not satisfied. Error B300.2: Restriction 2 is not satisfied.
In both cases, RES is set equal to zero and LRL is set equal to .FALSE., and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, (Academic Press, New York 1980) Sect. 2.26