Srivastava, H.M.Agarwal, A. K.2009-09-042009-09-0419862009-09-04http://hdl.handle.net/1828/1738Some simple ideas are used here to prove a theorem on generating functions for a certain class of q-polynomials. This general theorem is then applied to derive a fairly large number of known as well as new generating functions for the familiar q-analogues of various polynomial systems including, for example, the classical orthogonal polynomials of Hermite, Jacobi, and Laguerre. A number of other interesting consequences of the theorem are also discussed.engenerating functionsq-polynomialsclassical orthogonal polynomialsq-serieshypergeometric identitiesquadratic transformationsspecial functionsq-Pfaff transformationKummer's summation theoremGauss's second theoremPfaff-Saalschutz theorembasic (or q-) hypergeometric functionGaussian polynomial (or q-binomial coefficient)q-binomial theoremq-Laguerre polynomialslittle q-Jacobi polynomialsq-Hahn polynomialsq-Meixner polynomialsq-Charlier polynomialsHeine's transformationconfluent hypergeometric functionq-Hermite polynomialsq-summation formulaq-hypergeometric polynomialsTechnical Report