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Integrate problem

• To: mathgroup at yoda.physics.unc.edu
• Subject: Integrate problem
• From: Fasol <fasol at tansei.cc.u-tokyo.ac.jp>
• Date: Thu, 28 Jan 93 17:52:38 JST

Dear Mathgroup:

I tried to solve the integral

Integrate[Cos[kr Cos[phi]],{phi,0,2 Pi}] 

using Mma 2.1 on a Macintosh. It turns out, that this integral
is equal to 

2 Pi BesselJ[0,kr].

Nevertheless, I could not get Mma to give me this result, 
Mathematica just returned the unevaluated expression after a while.
(I did load the integration packages, as suggested in November 1992
by Tom Wickham-Jones in a discussion in mathgroup, but involving
the different integral Integrate[BesselJ[0,k r], {r,0,Infinity}]).

Of course, I do not expect Mma to solve each and every
integral, but maybe somebody knows a trick I overlooked or 
recognizes a mistake I made - or maybe this will work in a
future update of Mma.

From:
Gerhard Fasol
fasol at tansei.cc.u-tokyo.ac.jp