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Re: Simplification of Hypergeometric Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84638] Re: [mg84613] Simplification of Hypergeometric Function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 7 Jan 2008 07:28:49 -0500 (EST)
  • Reply-to: hanlonr at cox.net

(LegendreP[n, m, 2, z] // FunctionExpand) /. m -> 0

Hypergeometric2F1[-n, n + 1, 1, (1 - z)/2]

% == (LegendreP[n, m, 3, z] // FunctionExpand) /. m -> 0

True

%% == LegendreP[n, z] // FullSimplify

True

repl = Hypergeometric2F1[-n_, n_ + 1, 1, z_] :>
   
   LegendreP[n, 1 - 2 z];

Hypergeometric2F1[-n, n + 1, 1, (1 - z)/2] /. repl

LegendreP[n, z]


Bob Hanlon

---- Fabian <NOSPAM_fahasch at yahoo.de> wrote: 
> How can one simplify 
>   Hypergeometric2F1[-n, 1 + n, 1, (1- z)/2]
> to the more elementary function LegendreP using Mathematica?
> 
> Fabian
> 



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