plegendre_d1.doc

Compute all the unnormalized Legendre polynomials and first derivatives.

Usage
-----
p, dp = PLegendre_d1 (lmax, z)

Returns
-------
p : float, dimension (lmax+1)
    An array of unnormalized Legendre polynomials up to degree lmax. Degree l
    corresponds to array index l.
dp : float, dimension (lmax+1)
    An array of the first derivatives of the unnormalized Legendre polynomials
    up to degree lmax. Degree l corresponds to array index l.

Parameters
----------
lmax : integer
    The maximum degree of the Legendre polynomials to be computed.
z : float
    The argument of the Legendre polynomial.

Description
-----------
PLegendre_d1 will calculate all of the unnormalized Legendre polynomials and
first derivatives up to degree lmax for a given argument. These are calculated
using a standard three-term recursion formula, and the integral of the Legendre
polynomials over the interval [-1, 1] is 2/(2l+1). Note that the derivative of
the Legendre polynomials is calculated with respect to its arguement z, and not
latitude or colatitude. If z=cos(theta), where theta is the colatitude, then it
is only necessary to multiply dp by -sin(theta) to obtain the derivative with
respect to theta.