| HOME | DOWNLOAD | DOCUMENTATION | FAQ |
> Home > Documentation > Python > Legendre Functions
PlSchmidt_d1
Compute all the Schmidt-normalized Legendre polynomials and first derivatives.
Usage
p, dp = PlSchmidt_d1 (lmax, z)
p: float, dimension (lmax+1)- An array of Schmidt-normalized Legendre polynomials up to degree
lmax. Degreelcorresponds to array indexl. dp: float, dimension (lmax+1)- An array of the first derivatives of the Schmidt-normalized Legendre polynomials up to degree
lmax. Degreelcorresponds to array indexl.
Parameters
lmax:integer- The maximum degree of the Legendre polynomials to be computed.
z: float- The argument of the Legendre polynomial.
Description
PlSchmidt_d1 will calculate all of the Schmidt-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 Schmidt-normalized 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.
See also
plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1, plschmidt, plmschmidt, plmschmidt_d1, plegendre, plegendre_d1, plegendrea, plegendrea_d1
> Home > Documentation > Python > Legendre Functions
| Laboratoire Lagrange | Observatoire de la Côte d'Azur | © 2017 SHTOOLS |