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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

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?