Michael J. Schlosser
Bilateral q-ultrasperical functions
(12 pages)
Abstract.
We introduce a bilateral extension of the continuous q-ultraspherical
polynomials which we call bilateral q-ultraspherical functions.
These functions are given as specific bilateral basic hypergeometric
2Ψ2 series, they are analytic in a variable
x = cos θ
and depend on two parameters β and γ and on a base q.
For these bilateral q-ultraspherical functions we derive a
bilateral generating function, find a three-term recurrence
relation, explain how they behave
under the action of the Askey-Wilson divided difference operator,
and show that they satisfy a type of
shifted orthogonality.
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