Srivastava, H.M.2022-11-122022-11-1220222022Srivastava, H. M. (2022). “Some families of generating functions associated with orthogonal polynomials and other higher transcendental functions.” Mathematics, 10(20), 3730. https://doi.org/10.3390/math10203730https://doi.org/10.3390/math10203730http://hdl.handle.net/1828/14413In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.enlinear and bilinear generating functionsorthogonal polynomialsJacobi, Laguerre and Hermite polynomialsBessel polynomialshigher transcendental functionsLagrange's expansion theoremBailey's bilinear generating functionHille-Hardy formulaMehler's formulaoperational techniquesLaplace and inverse Laplace transformsRiemann-Liouville fractional derivativehypergeometric functionshypergeometric polynomialsArticleDepartment of Mathematics and Statistics