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Re: expansion of a complex exponential in terms of Bessel functions

• To: mathgroup at smc.vnet.net
• Subject: [mg82310] Re: expansion of a complex exponential in terms of Bessel functions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 17 Oct 2007 04:06:18 -0400 (EDT)
• References: <ff1pgh$8rm$1@smc.vnet.net>

Hi,

just write down the rule and don't use Sum[] because
otherwise Mathematica will simplify back the Sum[]

Regards
   Jens

P. S. Ramanujam wrote:
> Dear MathForum
> 
> Is there a way to expand a complex exponential function such as exp[i x_ Cos[y_]]
> in terms of Bessel functions in Mathematica? For example, 
> Exp[i a Cos[b]]->Bessel[0,b]+Sum[i^n Bessel[J[n,b](Exp[i n b]+Exp[-i n b])?
> 
> Regards
> 
> P. S. Ramanujam
>