Fast, accurate numerical evaluation of incomplete Planck integrals

Methods for computing the integral of the Planck blackbody function over a finite spectral range, the so-called incomplete Planck integral, are necessary to perform multigroup radiative transfer calculations. We present a comparison, in terms of speed and accuracy, of a wide array of approaches to numerically evaluating these integrals. Our results indicate that a direct rational polynomial approximation to these integrals has the best combination of accuracy and efficiency. We also present for the first time a derivation of the polylogarithm form of these integrals and show that modern approaches to polylogarithm evaluation are suitable for numerically evaluating incomplete Planck integrals. This article is dedicated to Prof. B.D. Ganapol, the Transport Cowboy, on the occasion of his retirement. • The first derivation of the polylogarithm form of the incomplete Planck integral is given. • A new rational approximation to these integrals is also given. • A computational study compares several different methods for evaluating these integrals in terms of speed and accuracy.