Generally, the background is calculated as a Chebyshev polynomial. In GSAS and GSAS-II they appear as follows. Again, background is treated as a Chebyshev polynomial of the first kind ("Handbook of Mathematical Functions", M. Abramowitz and IA. Stegun, Ch. 22), with intensity given by:
where are the coefficients of the Chebyshev polynomial taken from Table 22.3, pg. 795 of the Handbook. The coefficients have the form:
and the values for are found in the Handbook. The angular range () is converted to  to make the Chebyshev polynomial orthogonal by
And, the orthogonal range for this function is –1 to +1.