Some Generating Functions for a Class of Hypergeometric Polynomials

Some Generating Functions for a Class of Hypergeometric Polynomials

This article concerned with some new features for hypergeometric polynomials( ). ( , ) S x k Theresults obtained here contain the various families of multilinear and multilateral generatingfunctions, various features and some exceptions for these polynomials. We will also give atheorem to families giving certain bilateral generating functions for hypergeometric polynomials( )( , ) S x k and generalized Lauricella functions. Finally, we get a few interesting results for thisgiven theorem.

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  • Chen, K.Y., Srivastava, H.M, ‘‘A New Result For Hypergeometric Polynomials’’, Proceeding of The American Mathematical Society, 133, 3295-3302, (2005).
  • Srivastava, H.M., Manocha, H.L., ‘‘A Treatise on Generating Functions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1984).
  • Lauricella, G., ‘‘Sulle funzioni ipergeometriche a più variabili’’, Rend. Circ. Mat. Palermo 7, 111-158, (1893).
  • Srivastava, H.M., Daoust, M.C., ‘‘Certain generalized Neumann expansions associated with the Kampé de Fériet function’’, Nederl. akad. Westensch. Indag. Math. 31, 449-457, (1969).
  • Exton, H., ‘‘Multiple Hypergeometric Functions and Applicaions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1976).
  • Qureshi, M.I. , Khan, M.S., Pathan, M.A., ‘‘Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem’’, Internal J. Math. Math. Sci. 2005, 143-153, (2005).
  • Srivastava, H.M., Karlsson, P.W. , ‘‘Multiple Gaussian Hypergeometric Series’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1985).
  • Liu, S.-J., Lin, S.-D., Srivastava, H.M., Wong, M.-M., ‘‘Bilateral generating functions for the ErkusSrivastava polynomials and the generalized Lauricella functions’’, App. Mathematcis and Comp., 218, 7685-7693, (2012).
  • Aktaş, R. Şahin, R., Altın, A., ‘‘On a multivariable extension of the Humbert polynomials’’, Applied Mathematics and Computation, 218, 662-666, (2011).
  • Aktaş, R., Taşdelen, F., Yavuz, N., ‘‘Bilateral and Bilinear generating functions for the Generalized Zernike or disc polynomials’’, Ars Combinatoria, 108, 389-400, (2013).
  • Altın, A., Erkuş, E., Taşdelen, F., ‘‘The q-Lagrange polynomials in several variables’’ Taiwanese J. Math., 10(5): 1131-1137, (2006).
  • Srivastava, H.M., Taşdelen, F., Şekeroğlu, B., ‘‘Some families of generating functions for the qKonhauser polynomials’’, Taiwanese J. Math., 12(3): 841-850, (2008).
  • Erdélyi, A., Magnus, W., Oberhettinger F., Tricomi, F.G., ‘‘Higher Transcendental Functions’’, Vol. II, McGraw-Hill Book Company, New York, (1955).
  • Özmen, N., Erkuş-Duman, E., ‘‘On the Poisson-Charlier polynomials’’, Serdica Math. J. 41(4): 457- 470, (2015).
  • Özmen, N., Erkuş-Duman, E., ‘‘Some families of generating functions for the generalized Cesáro polynomials’’, J. Comput. Anal. Appl., 25(4): 670-683, (2018).