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MathGroup Archive 2006

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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.


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