Hermite transform

In mathematics, the Hermite transform is an integral transform named after the mathematician Charles Hermite that uses Hermite polynomials

n

( x )

{\displaystyle H_{n}(x)}

as kernels of the transform.

The Hermite transform

( x ) } ≡

of a function

{\displaystyle H\{F(x)\}\equiv f_{H}(n)=\int _{-\infty }^{\infty }e^{-x^{2}}\ H_{n}(x)\ F(x)\ dx}

The inverse Hermite transform

π