Summation Formulas for the product of the q-Kummer Functions from $E_q(2)$

Abstract

Using the representation of E_q(2) on the non-commutative space zz^*-qz^*z=σ; q<1, σ>0 summation formulas for the product of two, three and four q-Kummer functions are derived.

Latex, 8 pages

References in corpus (7)

• The q-harmonic oscillator and the Al-Salam and Carlitz polynomials
• The q-harmonic oscillator and an analog of the Charlier polynomials
• Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group
• Unitary representations of the 2-dimensional Euclidean group in the Heisenberg algebra
• Green Function on the q-Symmetric Space SU_q(2)/U(1)
• Green function on the quantum plane
• Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra