Implicit integration of finite alternating series of hypergeometric (2F1) functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg65400] Implicit integration of finite alternating series of hypergeometric (2F1) functions*From*: "Mark Smith" <dsummoner at hotmail.com>*Date*: Thu, 30 Mar 2006 05:29:53 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I am having a problem with Mathematica in determining a closed form analytical solution for the implicit integral of the following: -(a/Pi)*Cos[Pi*(t-b)/a]*Hypergeometric2F1[0.5,0.5*(1-n),1.5,(Cos[Pi*(t-b)/a])^2]*c + d In this equation the terms a, b, c and d are fixed constants for the problem. The term n is also a constant with value greater than zero. The term t is is the variable. Mathematica returns the input line, as an output line, without an evaluation. When I specify n, a priori, with respect to the integration operation, Mathematica has no problem with performing the integration. I would, however, like a closed form analytical solution or a family of solutions without the a priori specification of n. Any help would be greatly appreciated.