Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO, Wakhare, Tanay V.
Si
Symmetry-Basel
Article
Científica
2.143
01/12/2018
000454725100096
2-s2.0-85059005656
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesaro 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)phi(5), (5)phi(5), (4)phi(3), (3)phi(2), (2)phi(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.
basic hypergeometric functions; generating functions; q-polynomials