On binomial operator representations of certain polynomials
DOI:
https://doi.org/10.4067/S0716-09172011000200001Keywords:
Binomial operator, Operational represenations.Abstract
Based on the technique used by M.A.Khanand A. K. Shukla [4] here finite series representations of binomial partial differential operators have been used to establish operator representations of various polynomials not considered in the earlier mentioned paper. The results obtained are believed to be new.References
[1] Andrews, G. E., Askey, R. and Roy, R.: Special functions. Cambridge University Press, (1999).
[2] Bedient,P. E.: Polynomials related to Appell functions of two variables. Michigan thesis, (1958).
[3] Chihara, T. S.: An introdution to Orthogonal Polynomials. Gordon and Breach, New York, (1978).
[4] Khan, M. A. and Shukla, A. K.: On Binomial and Trinomial operator representations of certain Polynomials. Italian Journal of Pure and Applied Mathematics- N. 25, pp. 103-110, (2009).
[5] Khan, M. A. and Nisar K. S. : On bilinear operator representations of Laguerre and Jacobi polynomials. International transactions in Applied Sciences, 1, pp. 521-526, (2009).
[6] Khan, M. A. and Nisar K. S.: Bilinear and Bilateral summation formulae of certain polynomials in the form of operator representations. Accepted for publication in Thai J. Mathematics, (2010).
[7] Khan, M. A. and Nisar K. S.: On operator representations of various polynomials using the operator of W.A. Al-Salam. Int. J. Computational and Applied Math., Volume 5, N 3, pp. 393-405, (2010).
[8] Khan, M. A. and Nisar K. S.: Operationalrepresentations of Bilinear and Bilateral Generating formulae for polynomials. Mathematical Sciences and Engg Applications, 3, pp. 1-19, (2010).
[9] Rainville, E. D.: Special Functions, MacMillan, New York (1960), Reprinted by Chelsea Publishing Company, Bronx, New York (1971).
[10] Srivastava, H. M. and Manocha, H. L. : A Treatise on Generating Functions, Ellis Horwood Limited, Chichester, (1984).
[2] Bedient,P. E.: Polynomials related to Appell functions of two variables. Michigan thesis, (1958).
[3] Chihara, T. S.: An introdution to Orthogonal Polynomials. Gordon and Breach, New York, (1978).
[4] Khan, M. A. and Shukla, A. K.: On Binomial and Trinomial operator representations of certain Polynomials. Italian Journal of Pure and Applied Mathematics- N. 25, pp. 103-110, (2009).
[5] Khan, M. A. and Nisar K. S. : On bilinear operator representations of Laguerre and Jacobi polynomials. International transactions in Applied Sciences, 1, pp. 521-526, (2009).
[6] Khan, M. A. and Nisar K. S.: Bilinear and Bilateral summation formulae of certain polynomials in the form of operator representations. Accepted for publication in Thai J. Mathematics, (2010).
[7] Khan, M. A. and Nisar K. S.: On operator representations of various polynomials using the operator of W.A. Al-Salam. Int. J. Computational and Applied Math., Volume 5, N 3, pp. 393-405, (2010).
[8] Khan, M. A. and Nisar K. S.: Operationalrepresentations of Bilinear and Bilateral Generating formulae for polynomials. Mathematical Sciences and Engg Applications, 3, pp. 1-19, (2010).
[9] Rainville, E. D.: Special Functions, MacMillan, New York (1960), Reprinted by Chelsea Publishing Company, Bronx, New York (1971).
[10] Srivastava, H. M. and Manocha, H. L. : A Treatise on Generating Functions, Ellis Horwood Limited, Chichester, (1984).
Published
2011-12-10
How to Cite
[1]
M. A. Khan and K. S. Nisar, “On binomial operator representations of certain polynomials”, Proyecciones (Antofagasta, On line), vol. 30, no. 2, pp. 137-148, Dec. 2011.
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