Integrating special functions

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• Subject: [mg131575] Integrating special functions
• From: Herman <btta2010 at gmail.com>
• Date: Sat, 7 Sep 2013 06:03:11 -0400 (EDT)
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```Dear All,

I would like to integrate the following function with Legendre polynomial and Gamma function. I am open to any suggestions.

ass = {s > 0, \[Alpha] > 0};

\[Phi][s_, x_, \[Alpha]_] := (-1)^s Sqrt[(s \[Alpha])/
Gamma[1 + 2*s]] LegendreP[s, s, Tanh[\[Alpha] x]]

\[Phi]1[s_, x_, \[Alpha]_] := D[[\[Phi][s, x, \[Alpha]], x]]

a3 = Table[
Integrate[-\[ImaginaryI] x \[Phi][s, x, a] \[Phi]1[s, x,
a], {x, -\[Infinity], \[Infinity]}, Assumptions -> \[Alpha] > 0,
s > 0]
would it be possible to get a closed form of the integration a3?

```

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