Role of Legendre Polynomial in Some PhysicalProblems

Abstract

In this thesis a brief review of some special functions interesting in physics, such as r, Hermite, and Legendre functions.

In the introduction a historical review of associated Legendre polyamial, its responsibility of appearance of two quantum numbers L,m and their complex expressions. In chapter I description of r function as Euler definition, Weirestrass and Factorial definitions.

Also description of Hermite polynomial, its application in harmonic oscillator problem. In chapter II details of properties of Legendre polynomials; orthogonal, normalization; and how any function F(z) could be represented as a power series in terms of Legendre polynomial.

In chapter Ill a brief presentation of some applications of Legendre polynomial in physics, e.g. in scattering theory in high energy hysics and gravitation. We have chosen two examples to describe in detail.

One of them depends on the generating function of Legendre polynomial (in electromagnetic theory).