Re: Integration result depends on variable name / problem with BesselJ Integral representation

*To*: mathgroup at smc.vnet.net*Subject*: [mg127200] Re: Integration result depends on variable name / problem with BesselJ Integral representation*From*: "Kevin J. McCann" <kjm at KevinMcCann.com>*Date*: Sat, 7 Jul 2012 05:29:45 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

This is a real issue. I tried the integrals as you suggested below, and indeed, I get the same results. If, however, I change psi to the Greek letter psi in the first version, I get zero. Not sure what is going on, but it is a bug. Kevin On 7/2/2012 10:24 PM, richardw at gmx.at wrote: > Dear all, > > the following integral is the integral representation of the bessel function of first kind, second order. But mathematica (8.0.4.0) gives me wrong results, depending on the variable name, it seems: > first with x: > Integrate[Sin[2 x] Exp[I t Cos[x - psi]], {x, 0, 2 \[Pi]}] > (8 I (-t Cos[t] + Sin[t]))/t^2 > > then x substituted with p: > Integrate[Sin[2 p] Exp[I t Cos[p - psi]], {p, 0, 2 \[Pi]}] > 0 > > How can the result depend on the variable name? There are no values assigned to x or p. The analytically obtained solution should be > 2 \[Pi] I^2 BesselJ[2, t] Sin [2 psi] > > Regards, > Richard >