Legendre Polynomials and Related Functions

Abstract

Abstract The Legendre polyrwmials are closely associated with physical phen omena for which spherical geometry is important. In particular, these polynomials first arose in the problem of expressing the newtonian potential of a conservative force field in an infinite series involving the distance variables of two points and their included central angle (see Sec. 4.2). Other similar problems dealing with either gravita tional potentials or electrostatic potentials also lead to Legendre polynomials, as do certain steady-state heat conduction problems in spherical solids, and so forth.