Abstract
Key Words: The Cauchy operator generating function , Mehler’s formula Rogers formula extended generating function extended Mehler’s formula
References:
[1] Abdlhusein M. A., ''The Operators and Rogers-SzegÖ polynomials'', M.Sc. Thesis, University of Basrah, Basrah, Iraq, (2009).
[2] Abdlhusein M. A., ''The basic and extended identities for certain polynomials'' Journal of College of Education for Pure Sciences, (2), pp. 11-23, (2012).
[3] Abdlhusein M. A., ''Representation of some series by the exponential operator w !" '' Journal of Missan Researches, (18), pp. 355-362, (2013).
[4] Abdlhusein M. A., ''The Euler operator for basic hypergeometric series'' Int. J. Adv. Appl. Math. and Mech., (2), pp. 42 – 52, (2014).
[5] Carlitz L., ''Generating functions for certain orthogonal polynomials'' Collectanea Mathematics, (23), pp. 91-104, (1972).
[6] Cao J., ''New proofs of generating functions for Rogers-SzegÖ polynomials'' Applied Mathematics and Computation, (207), pp. 486-492, (2009).
[7] Chen W.Y.C. and Liu Z. G., ''Parameter augmenting for basic hypergeometric series, II'' J. Combin. Theory, Ser. A (80) pp. 175–195, (1997).
[8] Chen W.Y.C. and Liu Z. G., ''Parameter augmenting for basic hypergeometric series, I'' Mathematical Essays in Honor of Gian-Carlo Rota, Eds., B. E. Sagan and R. P. Stanley, Birkhäuser, Boston, pp. 111129, (1998).
[9] Chen W.Y.C., Fu A.M. and Zhang B.Y., ''The homogeneous difference operator'' Adv. Appl. Math., (31), pp. 659–668, (2003).
[10] Chen W.Y.C., Saad H.L. and Sun L.H., ''The bivariate Rogers-SzegÖ polynomials'' J. Phys. A: Math. Theor., (40), pp. 6071–6084, (2007).
[11] Chen V.Y.B. and Gu N.S.S., ''The Cauchy operator for basic hypergeometric series'' Adv. Appl. Math., (41), pp. 177–196, (2008).
[12] Gasper G. and Rahman M., ''Basic Hypergeometric Series'', 2nd Ed., Cambridge University Press, Cambridge, MA, (2004).
[13] Saad H. L. and Abdlhusein M. A., ''The -exponential operator and generalized Rogers- SzegÖ polynomials'' Journal of Advances in Mathematics, (8), pp. 1440-1455, (2014).
[14] Saad H. L. and Sukhi A. A., ''Another homogeneous -difference operator'' Applied Mathematics and Computation, (215), pp. 4332-4339, (2010).
[15] Saad H. L. and Sukhi A. A., ''The q-Exponential Operator'' Applied Mathematical Sciences, (7) pp. 6369 – 6380, (2010).
[16] Zhang Z. Z. and Wang J., ''Two operator identities and their applications to terminating basic hypergeometric series and integrals'' J. Math. Anal. Appl., (312), pp. 653–665, (2005).