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B300 An integral of type

Routine ID: B300
Author(s): Library: MATHLIB
Submitter: Submitted: 15.03.1993
Language: FortranRevised:

Subroutine subprograms RSRTNT and DSRTNT calculate, based on indefinite integration, the definite integral
I(k,n;a,b,c;u,v) = uv{xk dx(a+bx+cx2)n},

for k=-3,-2,-1,0,1,2,3 and n=1,3, provided that a+bx+cx2> 0 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 (N002), ABEND (Z035)

Usage:

For t=R (type REAL), t=D (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+bx+cx2 .
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 LRL = .TRUE. , 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. |A|+|B|+|C| ≠0.

2. |K| ≤3 ; N = 1 or N = 3 .

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

Equations and Special Functions

C200



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Next: C200 Zero of Up: CERNLIB Previous: B105 Value of


Janne Saarela
Mon Apr 3 15:06:23 METDST 1995