MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Integral representation of Bessel functions


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


  • Prev by Date: Color grid with x and y args to visualize effects of 2D transformations?
  • Next by Date: Re: Another point about Mathematica 8.0
  • Previous by thread: Re: Color grid with x and y args to visualize effects of 2D transformations?
  • Next by thread: Re: Integral representation of Bessel functions