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beta function vs. sine

Marko Riedel 390 Maple
March 21 2013
2

Dear friends,

I am reporting with a brief comment concerning the integral int(1/(1+x^a), x=0..infinity) with a>=2 a real number. This was evaluated here.

Now Maple 15 (X86 64 LINUX) will quite happily compute this in its most simple form involving the sine when a is not a positive integer or a rational number. If it is, however, a beta function term results, which the simplifier does not know how to turn into a sine term even though the two arguments add up to one.

This is just to bring this to your attention. One might say that a beta function term is as good as a sine term, I would argue, though, that the sine term should be preferred. Maple will output the correct result when a is left unspecified (symbol), which I think is very nice.

Happy computing.

Marko Riedel
integral integer pi residue contour

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