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)