RE: Change of Variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg32523] RE: [mg32509] Change of Variables*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 25 Jan 2002 02:57:54 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

John, Here is one method. planck = 2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T)) - 1)^(-1); Solve[x == h*(c/(lambda*k*T)), lambda][[1,1]] lambda -> (c*h)/(k*T*x) planck /. lambda -> (c*h)/(k*T*x) (2*k^5*Pi*T^5*x^5)/(c^3*(-1 + E^x)*h^4) David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: John S [mailto:bosniajohns at hotmail.com] To: mathgroup at smc.vnet.net > > 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. > > >