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Mathematica code for change of variable

• To: mathgroup at smc.vnet.net
• Subject: [mg115313] Mathematica code for change of variable
• From: Lynn Bu <bu.lynn5 at gmail.com>
• Date: Fri, 7 Jan 2011 04:10:27 -0500 (EST)

Hello,

I work in Mathematica 7.0 and would like to know how to solve for S(B):

given that S(t) = Integral[p(x,t) Log[p(x,t)]dx, (-infinity,
infinity)] and p(x,t) = (1/ct) F(x/ ct).

There is a change of the variable x into:
 y =  x/ ct

In which case S(B) looks like:

S(B) = A + cB

for A = Integral[dy F(y) Ln[F(y)], (-infinity, infinity)]

and  B = Ln(t)

This is of course easier to solve by hand but I need a way to
demonstrate in Mathematica. I used "Solve", combining first two
equations, etc, however I was not successful.

Thanks if you can help,
L.B.