 
 
 
11.4.1  Legendre polynomials
The Legendre polynomial L(n,x) of degree n is a polynomial solution of the
differential equation
| (x2−1) y′′−2 x y′−n(n+1) y=0. | 
The Legendre polynomials satisfy the recurrence relation:
These polynomials are orthogonal for the scalar product:
The legendre
command finds the Legendre polynomials.
- 
legendre takes one mandatory argument and one
optional argument:
- 
n, an integer.
- Optionally, x, a variable name (by default
x).
 
- legendre(n  ⟨,x⟩) returns the Legendre
polynomial of degree n.
Examples
 
 
