laguerre( n , z )
The Laguerre polynomial of z in SageMath. Defined by
\[ L_n(z) = \frac{ 1 }{ n! } e^z \frac{ d^n }{ dz^n } ( z^n e^{-z} ) \]A solution of the differential equation
\[ z \frac{ d^2 f }{ dz^2 } + ( 1 - z ) \frac{ d f }{ dz } + n f = 0 \]Equivalent to gen_laguerre( n , 0 , z ).
Explicit form:
Plot on the real axis:
Special values:
Related functions: gen_laguerre
Function category: orthogonal polynomials sagemath-docs