Integral representation of Bessel functions
- To: mathgroup at smc.vnet.net
- Subject: [mg116551] Integral representation of Bessel functions
- From: John Travolta Sardus <pireddag at gmail.com>
- Date: Sat, 19 Feb 2011 05:14:12 -0500 (EST)
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