legendre¶
Can calculate the first several Legendre polynomials, along with (some of) their first derivatives.
-
climlab.utils.legendre.
P2
(x)[source]¶ The second Legendre polynomial.
\[P_2(x) = \frac{1}{2} (3x^2 - 1)\]
-
climlab.utils.legendre.
Pn
(x)[source]¶ Calculate Legendre polyomials P0 to P28 and returns them in a dictionary
Pn
.Parameters: x (float) – argument to calculate Legendre polynomials Return Pn: dictionary which contains order of Legendre polynomials (from 0 to 28) as keys and the corresponding evaluation of Legendre polynomials as values. Return type: dict
-
climlab.utils.legendre.
Pnprime
(x)[source]¶ Calculates first derivatives of Legendre polynomials and returns them in a dictionary
Pnprime
.Parameters: x (float) – argument to calculate first derivate of Legendre polynomials Return Pn: dictionary which contains order of Legendre polynomials (from 0 to 4 and even numbers until 14) as keys and the corresponding evaluation of first derivative of Legendre polynomials as values. Return type: dict