Introduction to Legendre Polynomials and Functions

Legendre Polynomials and Functions

• Legendre Polynomials and Functions:Legendre functions occur in problems of gravitational potential at point due to a unit mass at certain other point.This function is used in problems of potential theory when the natural boundaries are spheres with Center at the origin of co-ordinate.
  
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Legendre Polynomials and Functions:

Legendre Polynomial and Functions

• The equation
  (1-x^{2})\frac{d^{2}y}{dx^{2}}-2x\frac{dy}{dx}+n(n+1)y=0…(1)
  is called the Legendred’s differential equation. This equation arises in the solution of boundary value problems involving spherical symmetry.
  A series of (1) will be developed in the next section.
  Generating Functions

Legendre Polynomials and Functions

Legendre Polynomial and Functions(Generating Functions)

• In this article, Legendre polynomials and functions have been told