gen_laguerre( n , a , z )

The generalized or associated Laguerre polynomial of z in SageMath. Defined by

\[ L_n^a(z) = \frac{ 1 }{ n! } z^{-a} e^z \frac{ d^n }{ dz^n } ( z^{n+a} e^{-z} ) \]

A solution of the differential equation

\[ z \frac{ d^2 f }{ dz^2 } + ( a + 1 - z ) \frac{ d f }{ dz } + n f = 0 \]

Explicit form:

Plot on the real axis:

Special values:

Related functions:   laguerre

Function category: orthogonal polynomials sagemath-docs