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Updated: Aug 15, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Some Generating Functions for q-Polynomials
Howard S Cohl1, Roberto S Costas-Santos2, Tanay V Wakhare3
1Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA.
Abstract:
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series 4 ϕ 5, 5 ϕ 5, 4 ϕ 3, 3 ϕ 2, 2 ϕ 1, and q-Pochhammer symbols. Starting with our q-generating functions, we are also able to find some new classical generating functions for the Pasternack and Bateman polynomials.
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