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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)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
*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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