Combinatorics(?) notation question - sci.math

Message from discussion Combinatorics(?) notation question

Raymond Manzoni

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More options Jul 24, 3:59 pm

Newsgroups: sci.math

From: Raymond Manzoni <raym...@free.fr>

Date: Thu, 24 Jul 2008 09:59:49 +0200

Local: Thurs, Jul 24 2008 3:59 pm

Subject: Re: Combinatorics(?) notation question

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fjbl...@yahoo.com a écrit :

> Hi folks,

> I came across a piece of notation that I haven't seen before, and I'm
> wondering if it has a name. It's a function denoted (a,n) where n is
> an integer and a is a real number, usually an integer or half-
> integer. (It appears in coefficients for expansions of Bessel
> functions.) A couple of equivalent definitions for it are:

> (a,n) = Gamma(a+n+1/2)/(n! Gamma(a-n+1/2))

Hi,

In Watson's "Theory of Bessel functions" it appears in page 198 and
is introduced with the wording "If, following Hankel, we write (v,m)=
...= Gamma(v+m+1/2)/(m!*Gamma(v-m+1/2))" so that I had suggested 'Hankel
symbol' if... it had not been known this way :-) :
http://mathworld.wolfram.com/HankelsSymbol.html
(unsimplified formulation by the way...)

Hoping it helped,
Raymond

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