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expansion of a complex exponential in terms of Bessel functions

• To: mathgroup at smc.vnet.net
• Subject: [mg82244] expansion of a complex exponential in terms of Bessel functions
• From: "P. S. Ramanujam" <p.s.ramanujam at risoe.dk>
• Date: Tue, 16 Oct 2007 03:25:05 -0400 (EDT)

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