Extended Sunyaev Zel'dovich Distortion

Here is a Planck Distribution



This is the 2nd order distortion written in a simple form



which we check agrees with above formulae



This is the 1st order (classical) distortion



Here we define simpler forms for the 2 different pieces





which we check



Rayleigh-Jeans Limit
Plots of Brightness
Plots of Brightness Temperature
Frequency of Zero Distortion
Document converted by Mathematica of Wolfram Research