In mathematics, the Askey scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in Andrews & Askey (1985), the Askey scheme was first drawn by Labelle (1985) and by Askey and Wilson (1985), and has since been extended by Koekoek & Swarttouw (1998) and Koekoek, Lesky & Swarttouw (2010) to cover basic orthogonal polynomials.

## Askey scheme for hypergeometric orthogonal polynomials

Koekoek, Lesky & Swarttouw (2010, p.183) give the following version of the Askey scheme:

4F3
Wilson Racah
3F2
Continuous dual Hahn Continuous Hahn Hahn dual Hahn
2F1
Meixner–Pollaczek Jacobi Pseudo Jacobi Meixner Krawtchouk
2F0/1F1
Laguerre Bessel Charlier
1F0
Hermite

## Askey scheme for basic hypergeometric orthogonal polynomials

Koekoek, Lesky & Swarttouw (2010, p.413) give the following scheme for basic hypergeometric orthogonal polynomials:

4$\phi$3
3$\phi$2
2$\phi$1
2$\phi$0/1$\phi$1
1$\phi$0