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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 16.7 QAWC adaptive integration for Cauchy principal values

Function: int gsl_integration_qawc (gsl_function * f, double a, double b, double c, double epsabs, double epsrel, size_t limit, gsl_integration_workspace * workspace, double * result, double * abserr)
This function computes the Cauchy principal value of the integral of f over (a,b), with a singularity at c,
I = \int_a^b dx f(x) / (x - c)


The adaptive bisection algorithm of QAG is used, with modifications to ensure that subdivisions do not occur at the singular point x = c. When a subinterval contains the point x = c or is close to it then a special 25-point modified Clenshaw-Curtis rule is used to control the singularity. Further away from the singularity the algorithm uses an ordinary 15-point Gauss-Kronrod integration rule.

 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition