Compute all the 4-pi (geodesy) normalized Legendre polynomials and first derivatives.

## Usage

p, dp = PlBar_d1 (lmax, z)

## Returns

p : float, dimension (lmax+1)
An array of 4-pi (geodesy) normalized 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 4-pi (geodesy) normalized Legendre polynomials up to degree lmax.

## Parameters

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

## Description

PlBar_d1 will calculate all of the 4-pi (geodesy) normalized 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 geodesy-normalized Legendre polynomials over the interval [-1, 1] is 2. 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.