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Strange results from Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg74998] Strange results from Mathematica
• From: "Jung-Tsung Shen" <jushen at gmail.com>
• Date: Fri, 13 Apr 2007 02:16:16 -0400 (EDT)

Hi, I encountered a rather strange results from Mathematica today.

When evaluating the following integration

(1) Integrate[x (BesselJ[0, x])^2, {x,0, infinity}]

my Mathematica gave the answer 0. That's very weird, since if you plot
out the function x (BesselJ[0, x])^2, apparently the integral should
not be zero ...

Moreover, for the following integration

(2) Integrate[ (BesselJ[0, x])^2, {x,0, infinity}]

My Mathematica says it's some finite value. However, once you did
this, and then did (1), and then came back to do (1), the answer
became 0 ...

My Mathematica version is 5.0.1.0 on Mac Powerbook.

Thanks.

JT