Comparison With Challinor and Lasenby

Challinor and Lasenby (astro-ph/9711028) give the following formula for SZ20 (from their eq 2.14)

which we verify is equivalent to our computation

Challinor and Lasenby have also computed the next order term

To check that we have transcribed it correctly check that the Rayleigh-Jeans limit is correct

So the according to Challinor and Lasenby the 3rd order S-Z distortion is

Now plot the order results

and comparing with Rephaeli' s numerical results