Continuous q-Hahn polynomials

In mathematics, the continuous q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs give a detailed list of their properties.

Definition

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

$p_n(x;a,b,c,d|q)=a^{-n}{e}^{-inu}(ab{e}^{2iu},ac,ad;q{)}_n{}_4{\varphi }_3(q^{-n},abcd{q}^{n-1},a{e}^{i(t+2u)},a{e}^{-it};ab{e}^{2iu},ac,ad;q;q)$

$x=\cos (t+u)$

Gallery

CONTINUOUS q hahn ABS COMPLEX3D Maple PLOT

CONTINUOUS q hahn IIM COMPLEX3D Maple PLOT

CONTINUOUS q hahn RE COMPLEX3D Maple PLOT

CONTINUOUS q hahn ABS density Maple PLOT

CONTINUOUS q hahn im density Maple PLOT

CONTINUOUS q hahn RE density Maple PLOT

References

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