Compute all the unnormalized Legendre polynomials and first derivatives.
p
, dp
= PLegendre_d1 (lmax
, z
)
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
.
lmax
: integer
: The maximum degree of the Legendre polynomials to be computed.
z
: float
: The argument of the Legendre polynomial.
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
.
plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1, plschmidt, plschmidt_d1, plmschmidt, plmschmidt_d1, plegendre, plegendrea, plegendrea_d1