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Let $n$ be half an odd integer, say $n=k+1/2, k \in \mathbb{N}$.

Let $q\geq 1$. I would like to calculate (or approximate) the following integral: $$ \int_0^{\infty}\left(\sqrt{\frac{\pi}{2}}\cdot 1\cdot 3\cdot 5\cdots (2k+1) \frac{J_{k+\frac 12}(t)}{t^{k+ \frac 12}}\right)^q t\ dt. $$

Any ideas or references will be very helpful.

Thank you.

  • 0
    Maybe the explicit statement of the function $J$ could be helpful?2012-05-27
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    @awllower: Which ine would you propose?I've tried few representations-did not work. Thank you.2012-05-27
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    @Jack: I don't know if [tag:bessel] is a good tag name. I also don't think that adding new tags should be done without consulting the community via the [meta] site.2014-08-30
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    @AsafKaragila: good point, I'll post a proposal on Meta to create a specific tag for Bessel-functions-related questions.2014-08-30
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    Here it is: http://meta.math.stackexchange.com/questions/16695/about-the-creation-of-a-bessel-functions-tag2014-08-30

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