Compute all the 4-pi (geodesy) normalized Legendre polynomials and first derivatives.
p
, dp
= pyshtools.PlBar_d1 (lmax
, z
)
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
.
lmax
: integer
: The maximum degree of the Legendre polynomials to be computed.
z
: float
: The argument of the Legendre polynomial.
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.
plbar
, plmbar
, plmbar_d1
, plon
, plon_d1
, plmon
, plmon_d1
, plschmidt
, plschmidt_d1
, plmschmidt
, plmschmidt_d1
, plegendre
, plegendre_d1
, plegendrea
, plegendrea_d1