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Little q Jacobi polynomials

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Little q-Jacobi polynomials

In mathematics, the little q-Jacobi polynomials pn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Hahn (1949). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Contents

Definition

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

p n ( x ; a , b ; q ) = 2 ϕ 1 ( q − n , a b q n + 1 ; a q ; q , x q )

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

References

Little q-Jacobi polynomials Wikipedia
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