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