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Change of Variables

• To: mathgroup at smc.vnet.net
• Subject: [mg32509] Change of Variables
• From: "John S" <bosniajohns at hotmail.com>
• Date: Thu, 24 Jan 2002 05:21:03 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I would greatly appreciate any help with the following problem.  I am trying
to perform a change of variable in a function/definition so that I can
integrate it.  In particular, I want to take Planck's Radiation Law:

planck=2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T))-1)^(-1)

and substitute x=h*c/(lambda*k*T) and integrate wrt lambda from 0 to
infinity.  I tried using replace, but that does not seem to try to
manipulate the function in terms of x, but simply seek out the replacement,
and if it exists, perform it.

An even simpler example is the following:

test=v/c
Replace[test^2,v/c -> beta]

does not yield beta^2, but rather v^2/c^2.

Again, any and all help would be greatly appreciated.

• Follow-Ups:
  • Re: Change of Variables
    • From: Daniel Lichtblau <danl@wolfram.com>