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## Re: [Help-gsl] qags, qagp, and qawc

**From**: |
Brian Gough |

**Subject**: |
Re: [Help-gsl] qags, qagp, and qawc |

**Date**: |
Thu, 15 Apr 2004 20:00:44 +0100 |

Nicolas Bock writes:
>* I tried to integrate 1/(x - x_0) with different limits, a and b, with *
>* qags, qagp, and qawc. Only qawc produced the correct answer for *
>* different choices of a and b, whereas qags and qagp sometimes worked *
>* and sometimes didn't. From the description of qags and qagp it wasn't *
>* quite clear to me if that's something to be expected or not. Should *
>* qags and qagp be able to integrate this type of singularity?*
Hello,
Hmmm... this singularity is not actually integrable, so QAGS and QAGP
are not suitable. Only integrable singularities are supported by
them. One can calculate the Cauchy principal value as a limit from
opposite sides of the singularity with QAWC though.
>* In another test I tried the integral 1 / (x - x_0)^2 and found to my *
>* surprise that qawc does not produce the right answer this time. Is it *
>* not able to handle singularities of higher order?*
QAWC only handles Cauchy principal values of 1/(x-x_0) integrals so it
will not work for any other case. I'm not sure what answer would be
expected for a 1/(x-x^0)^2 integral, except infinity, since it is a
purely positive singularity.
See the original QUADPACK book in the references for more details.
--
Brian Gough
Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/