change of variable newbie question

• To: mathgroup at smc.vnet.net
• Subject: [mg115077] change of variable newbie question
• From: Lynn Bu <bu.lynn5 at gmail.com>
• Date: Thu, 30 Dec 2010 04:12:06 -0500 (EST)

```Hi,

I work in Mathematica 7.0 and would like to know how to code according to
the integral:

S[t] = Integral[p[x,t]Log[p[x,t]]dx, {-infinity, infinity}]

Where:

p[x,t] = (1/t=CE=B4)F(x/ t=CE=B4)

There is a change of the variable x into:

y =  x/ t=CE=B4

In which case; the integral comes out to a form looking like:

S(=CF=84) = A + =CE=B4=CF=84

where:

A =E2=89=A1 Integral[dy F(y) Ln[F(y)], {-infinity, infinity}]

And

=CF=84 =E2=89=A1 Ln(t)

Would appreciate the assistance =E2=80=93 I tied a number of ways, Solve, combining
first two equations, etc. Note first equation is Shannon entropy form.

Thanks if you can help,

L.B.

```

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