TY - EJOU
AU - Cohl, Howard S.
AU - Costas-Santos, Roberto S.
AU - Wakhare, Tanay V.
TI - Some Generating Functions for q-Polynomials
T2 - Symmetry
PY - 2018
VL - 10
IS - 12
SN - 2073-8994
AB - 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.
KW - basic hypergeometric functions
KW - generating functions
KW - q-polynomials
DO - 10.3390/sym10120758