Two methods for the computation of the coefficients of the ultraspherical window are presented. The first corresponds to a concise exposition of Streit's method. The second is a new method that involves equating an ultraspherical window's frequency-domain representation to a Fourier series from which the coefficients are readily found. The two methods produce exactly the same results given the same window parameters. Also outlined is a method for the selection of an ultraspherical window's parameters based on the Dolph-Chebyshev window. This method highlights the flexibility of the ultraspherical window.