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
>

```

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