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

• To: mathgroup at smc.vnet.net
• Subject: [mg127206] Re: Integration result depends on variable name / problem with BesselJ
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sun, 8 Jul 2012 06:55:02 -0400 (EDT)
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• References: <jt8vk9\$k5c\$1@smc.vnet.net>

```On 7/7/2012 2:30 AM, Kevin J. McCann wrote:
> This is a real issue. I tried the integrals as you suggested below, and
> indeed, I get the same results.

Me too.  I tried this:

Timing[{Integrate[Sin[2 b] Exp[I t Cos[b - c]], {b, 0, 2 \[Pi]}],
Integrate[Sin[2 d] Exp[I t Cos[d - c]], {d, 0, 2 \[Pi]}]}]

returns

{148.562,{0,(8 I (-t Cos[t]+Sin[t]))/t^2}}

so the issue might be whether the variable of integration comes before
or after the other item inside the cosine.

Note that Cos[b-c]  simplifies to Cos[b-c]  but
Cos[d-c]  simplifies to Cos[c-d].

Since the sign of c is irrelevant in whatever Mathematica is doing
(wrong :)  ) and does not appear in the answer at all while it should..

we could just try this

Timing[{Integrate[Sin[2 b] Exp[I t Cos[b + c]], {b, 0, 2 \[Pi]}],
Integrate[Sin[2 d] Exp[I t Cos[d + c]], {d, 0, 2 \[Pi]}]}]

which returns  {28.453, {0, 0}}.

At least it was faster.

```

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