hermite( n , z )

The Hermite polynomial of z in SageMath. Defined by

\[ H_n(z) = (-1)^n e^{z^2} \frac{ d^n }{ dz^n } e^{-z^2} \]

A solution of the differential equation

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

Explicit form:

Plot on the real axis:

Special values:

Related functions:  

Function category: orthogonal polynomials sagemath-docs