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.