Relativistic corrections to the Sunyaev-Zel'dovich effect by A. D. Challinor and A. N. Lasenby

Primary theoretical research. Submitted in 1997; published in the Astrophysical Journal in 1998, DOI doi.org/10.1086/305623. The abstract explicitly gives the Rayleigh-Jeans decrement as $-2y$ times relativistic corrections.