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Integrating special functions

  • To: mathgroup at smc.vnet.net
  • 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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