Re: troublesome integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg126032] Re: troublesome integral*From*: Yi Wang <tririverwangyi at gmail.com>*Date*: Fri, 13 Apr 2012 04:51:57 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jm64ib$6la$1@smc.vnet.net>

Yes, this shouldn't be a hard integral. On my computer Mathematica cannot do it either. But there is a workaround: first let beta -> beta+alpha. Then the integral becomes =E2=88=AB cos[=CE=B2+=CE=B1] exp[ iz cos=CE=B2 ] d=CE=B2. Then expand cos[=CE=B2+=CE=B1] to cos[=CE=B2]cos[=CE=B1]-sin[=CE=B2]sin[=CE=B1]. Then Mathematica knows how to calculate. In[17]:= Integrate[ Cos[\[Alpha]] Cos[\[Beta]] Exp[I z Cos[\[Beta]]], {\[Beta], 0, 2 \[Pi]}, Assumptions -> z \[Element] Reals] Out[17]= 2 I \[Pi] BesselJ[1, z] Cos[\[Alpha]] In[18]:= Integrate[-Sin[\[Alpha]] Sin[\[Beta]] Exp[ I z Cos[\[Beta]]], {\[Beta], 0, 2 \[Pi]}, Assumptions -> z \[Element] Reals] Out[18]= 0 Thus the final result is the same as yours. Best, Yi On Thursday, April 12, 2012 4:42:51 AM UTC-4, peter lindsay wrote: > A couple of colleagues wondered about this. I've sent it on to support @ wolfram who are escalating it to the developers. Possibly someone here has an answer though ? > > Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta]-\[Alpha]]],{\[Beta],0,2 \[Pi]},Assumptions->z\[Element]Reals] > > doesn't seem to run. > > Answer should be > > 2 I \[Pi] BesselJ[1,z] Cos[\[Alpha]] [ I think ] > > thanks > > > Peter Lindsay