Legendre functions (pygeoid.sharm.legendre)

Legender polynomials and functions

pygeoid.sharm.legendre.lplm_d1(lmax, x)[source]

Associated Legendre functions of the first kind and their derivatives.

Parameters:
  • lmax (int) – Maximum degree and order.
  • x (float) – Input value.
Returns:

  • Plm(x) ((lmax + 1, lmax + 1) array) – Values of Plm(x) for all orders and degrees.
  • Plm_d(x) ({(lmax + 1, lmax + 1), None} array) – Values of Plm_d(x) for all orders and degrees. Will return None if x is very close or equal to -1 or 1.
pygeoid.sharm.legendre.lplm(lmax, x)[source]

Associated Legendre functions of the first kind.

Parameters:
  • lmax (int) – Maximum degree and order of the Plm(x).
  • x (float) – Input value.
Returns:

Plm(x) – Values of Plm(x) for all orders and degrees.
Return type:

(lmax + 1, lmax + 1) array