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 01:41:57 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*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.