q-Ultraspherical polynomials for q a root of unity

Abstract

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $s{o}_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of $q$-beta integrals of Ramanujan.

7 pages, LATEX

References in corpus (1)

• Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity

Cited by in corpus (4)

• Entanglement in Fermionic Chains and Bispectrality
• An SU(2) Analog of the Azbel--Hofstadter Hamiltonian
• Center of the universal Askey--Wilson algebra at roots of unity
• An algebraic interpretation of the intertwining operators associated with the discrete Fourier transform