Askey Scheme

Use case:

It is used to Orthogonal Basis functions for the Polynomial Chaos Expansion

Distribution	Basis function
Normal	Hermit Polynomial
Uniform	Legendre
Gamma	Laguerre
Beta	Jacobi

Example

Hermit Polynomial	Value
$H_0(\xi )$	1
$H_1(\xi )$	$\xi$
$H_2(\xi )$	${\xi }^2-1$
$H_3(\xi )$	${\xi }^3-3\xi$
$H_4(\xi )$	${\xi }^4-6{\xi }^2+3$
…	…