legendre

Can calculate the first several Legendre polynomials, along with (some of) their first derivatives.

climlab.utils.legendre.P0(x)

\[P_0 (x) = 1\]

climlab.utils.legendre.P1(x)

\[P_1 (x) = 1\]

climlab.utils.legendre.P2(x)

The second Legendre polynomial.

\[P_2(x) = \frac{1}{2} (3x^2 - 1)\]

climlab.utils.legendre.Pn(x)

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)

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