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MathGroup Archive 2012

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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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