An Effective Method for Calculating the Sum of an Infinite Series of Legendre Polynomials

Nichaphat Boonkorkuea, Vimolyut Varnasavang, Suporn Ratanapun

Abstract

To evaluate series of Legendre polynomials of the form , we find closed forms for Legendre polynomials that are good approximations for large n and are suitable for calculations on a personal computer of medium capacity. The convergence of an infinite series of Legendre polynomials is discussed.