Re: troublesome integral
- To: mathgroup at smc.vnet.net
- Subject: [mg126033] Re: troublesome integral
- From: danl at wolfram.com
- Date: Fri, 13 Apr 2012 04:52:18 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jm64ib$6la$1@smc.vnet.net>
On Thursday, April 12, 2012 3:42:51 AM UTC-5, 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 You can do this by translating so that the cosine in the exponential has a simple argument of 'b', recognizing that by periodicity you need not change the range of integration. In[190]:= Integrate[Cos[b + a] Exp[I*z*Cos[b]], {b, 0, 2*Pi}, Assumptions -> {Element[{a, z}, Reals]}] Out[190]= 2*I*Pi*BesselJ[1, z]*Cos[a] Daniel Lichtblau Wolfram Research