Legendre functions and polynomials
| Syntax: |
y = LEGENDRE(n,x)
|
The most elementary of the Legendre functions, the Legendre polynomials,
, can be defined by
the generating function:

More explicit representations are:

where
is the hypergeometric
function.
Unnormalized associated Legendre functions of degree n

Normalized associated Legendre functions

where
,
is a non-negative
integer and
satisfy the
differential equation:

Note that PLMU(n,0,x) = LEGENDRE(n,x)