Re: expansion of a complex exponential in terms of Bessel functions
- To: mathgroup at smc.vnet.net
- Subject: [mg83071] Re: expansion of a complex exponential in terms of Bessel functions
- From: "P. S. Ramanujam" <p.s.ramanujam at risoe.dk>
- Date: Fri, 9 Nov 2007 05:18:30 -0500 (EST)
For the case ruleA=Exp[I x_a Cos[y_]]->BesselJ[0,xa]+I^n BesselJ[n,xa](Exp[Iny]+Exp[-Iny])) Evaluate[Exp[I 3.14 a Cos[2 z]//.ruleA I do not get an expansion in terms of Bessel functions; instead I get Exp[3.14 I a Cos[2z]] However, if I leave out the Complex I from the exponential, ruleA=Exp[x_a Cos[y_]]->BesselJ[0,xa]+I^n BesselJ[n,xa](Exp[Iny]+Exp[-Iny])) Evaluate[Exp[3.14 a Cos[2 z]//.ruleA then I get BesselJ[0,3.14a]+I^n (Exp[-2 I n z]+Exp[2 I n z])BesselJ[n, 3.14 a] How can I get around this problem? Sincerely Ramanujam