Little q-Jacobi polynomials


In mathematics, the little q-Jacobi polynomials pn are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by. give a detailed list of their properties.

Definition

The little q-Jacobi polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by

Orthogonality

Recurrence and difference relations

Rodrigues formula

Generating function

Relation to other polynomials

Gallery

The following are a set of animation plots for Little q-Jacobi polynomials, with varying q;
three density plots of imaginary, real and modulus in complex space; three set of complex 3D plots
of imaginary, real and modulus of the said polynomials.