Polynomial expression and Epstein–Hubbell generalized elliptic-type integral

Abstract

When computing the radiation field off axis from a uniform circular disk source radiating according to an arbitrary angular distribution law, Hubbell and co-workers have encountered the integrals Ω j ( K 2). In this paper we have expressed the inverse of these integrals in the form of simple polynomials. The coefficients of these polynomials are obtained analytically. The results are given for values of K 2 varying from 0.08 to 0.88 for j=0–2. Results of a tenth degree polynomial are compared and are found to agree very well with the results obtained by numerically integrating the integral. If better accuracy is required, the degree of the polynomial can be increased.