Re: Integral representation of Bessel functions
- To: mathgroup at smc.vnet.net
- Subject: [mg116755] Re: Integral representation of Bessel functions
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Sat, 26 Feb 2011 06:07:29 -0500 (EST)
John Travolta Sardus wrote:
> I have tried an integral (version 8), I find a result that I do not
> agree with
>
> Assuming[x \[Element] Reals && \[Psi] \[Element] Reals,
> Integrate[
> Exp[I*(\[Phi] - \[Psi])]*
> Exp[I*x*Cos[(\[Phi] - \[Psi])]], {\[Phi], -\[Pi], \[Pi]}]]
>
> I obtain
>
> \[Pi] BesselJ[1, x] (I Cos[\[Psi]] + Sin[\[Psi]])
>
> While according to me it should be
>
> \[Pi] BesselJ[1, x]
>
> Or at least no dependence on \[Psi] must be present, as I can do a
> change of variable eliminating \[Psi] (the integral is on the whole
> circle and the function is periodic with period 2*\[Pi]). Do I make a
> mistake with the input? Do I read the output incorrectly? Or what
> else?
>
> Thanks in advance for any answer.
>
> Giovanni
>
Just to confirm, this is indeed a bug. Will get filed and fixed (either
to return a correct result, or, more likely, unevalauted).
Daniel Lichtblau
Wolfram Research