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MathGroup Archive 2000

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Re: Associated Legendre Definition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25668] Re: [mg25613] Associated Legendre Definition
  • From: BobHanlon at aol.com
  • Date: Wed, 18 Oct 2000 02:52:36 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 10/16/2000 3:28:00 AM, pmib at my-deja.com writes:

>In Mathematica, the associated Legendre polynomial is defined as
>
>P(n,m,x) = (-1)^m (1-x^2)^(m/2) d^m/dx^m (P(n,x))
>
>while in Schaum's Outlines 'Mathematical Handbook of Formulas and
>tables' it is defined as
>
>P(n,m,x) = (1-x^2)^(m/2) d^m/dx^m (P(n,x))
>
>What is true (or doesn't it matter)?
>

Many special functions have multiple definitions with slight variations. The 
definition which Mathematica uses is the same as that used in Abramowitz and 
Stegun (8.6.6) and in Gradshteyn and Ryzhik (8.752.1).


Bob Hanlon


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