6.30.1 Legendre polynomials: legendre
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
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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.
-
Input:
legendre(4)
Output:
- Input:
legendre(4,y)
Output: