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more contour integration issues

Marko Riedel 390 Maple
December 09 2012
1

Hello all,

I recently helped someone with a contour integration problem, you may find my calculation at the following link. It occurred to me to test this integral with Maple and Mathematica.

For example,

int(1/x^(1/3)/(x^2+2*x*cos(Pi/7)+1), x=0..infinity);

produces an unusable output from Mathematica. Maple is a little better, but does not recognize the simple end result.

The integral

int(1/x^(17/19)/(x^2+2*x*cos(Pi/7)+1), x=0..infinity);

seems to hang Maple, while Mathematica gives up after a long computation.

Finally, the integral

int(1/x^(1/2)/(x^2+2*x*cos(Pi/5)+1), x=0..infinity);

gets a correct answer from Maple while Mathematica produces something more cryptic.

I hope these observations are useful and that perhaps the case where Maple hangs can be fixed. As I said in an earlier message there is nothing wrong with adding a (sophisticated) table lookup to Maple's set of internal integration routines to catch cases like these.

Marko Riedel
integration contour

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