Little q-Jacobi polynomials

In mathematics, the little q-Jacobi polynomials p_n(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Template:Harvtxt. Template:Harvs give a detailed list of their properties.

Definition

The little q-Jacobi polynomials are given in terms of basic hypergeometric functions by

$p_n(x;a,b;q)={}_2{\varphi }_1(q^{-n},ab{q}^{n+1};aq;q,xq)$

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.

LITTLE q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT

LITTLE q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT

LITTLE q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT

LITTLE q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT

LITTLE q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT

LITTLE q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT

References

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