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
$H_1(\xi )$	$\xi$
$H_2(\xi )$	${\xi }^2-1$
…	…

LEGENDRE POLYNOMIAL	VALUE
$P_0(\xi )$	$1$
$P_1(\xi )$	$\xi$
$P_2(\xi )$	$\frac{1}{2}(3{\xi }^2-1)$
…	…