Fourier and other series containing associated Legendre functions for incomplete Epstein–Hubbell integrals and functions related to elliptic integrals

Abstract

Fourier series containing associated Legendre functions are given for functions related to the Legendre elliptic integrals and for incomplete Epstein–Hubbell integrals. A number of definite and indefinite integrals related to these series are derived. Additional series of Legendre functions and integrals are derived from a binomial expansion of the reciprocal of the delta amplitude. A power series expansion for the elliptic integral of the third kind in terms of the parameter α is obtained. Series of associated Legendre functions are given for general monomials.

Keywords:

• Epstein–Hubbell integrals
• Legendre functions
• Fourier series
• Elliptic integrals

Additional information

Notes on contributors

J. T. Conway

Email: [email protected]