Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 201-207, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


POLYNOMIAL SETS GENERATED BY e^tf(xt)?(yt)


Mumtaz Ahmad Khan¹
Bahman Alidad²

¹Aligarh Muslim University, India
²Golestan University, Iran


Correspondencia a:

Abstract

The present paper deals with two variables polynomial sets generated by functions of the form e^tf(xt)?(yt). Its special case analogous to Laguerre polynomials have been discussed.

References

[1] CHATTERJEA, S. K. A note on Laguerre polynomials of two variables, Bull. Cal. Math. Soc., Vol. 83, pp. 263, (1991).        [ Links ]

[2] KHAN, M. A. AND SHUKLA, A. K. On Laguerre polynomials of several variables, Bull. Cal. Math. Soc., Vol. 89, pp. 155-164, (1997).        [ Links ]

[3] KHAN, M. A. AND SHUKLA, A. K. A note on Laguerre polynomials of m variables, Bulletin of the Greek Mathematical Society., Vol. 40, pp. 113-117, (1998).        [ Links ]

[4] KHAN, M. A. AND ABUKHAMMASH, G. S. On Hermite polynomials of two variables suggested by S. F. Ragab’s Laguerre polynomials of two variables, Bull. Cal. Math. Soc., Vol. 90, pp. 61-76, (1998).        [ Links ]

[5] KHAN, M. A. AND AHMAD, K. On a general class of polynomials L_n^(a,ß;?,d) (x, y) of two variables suggested by the polynomials L_n^(a,ß) (x, y) of Ragab and L_n^(a,ß) (x) of Prabhakar and Rekha, Pro Mathematica, Vol. xix/Nos. 37-38, pp. 21-38, (2005).        [ Links ]

[6] KHAN, M. A. AND ALIDAD, B. Polynomial sets generated by functions of the form G(2xt - t²)K(2yt - t²) , Communicated for publication.        [ Links ]

[7] RAGAB, S. F. On Laguerse polynomials of two variables L_n^(a,ß) (x, y), Bull. Cal. Math. Soc., Vol. 83, pp. 253, (1991).        [ Links ]

[8] RAINVILLE, E. D. Special Functions, Macmillan, New York; Reprinted by Chelsea Publ. Co., Bronx., New York, (1971).        [ Links ]

[9] SRIVASTAVA, H. M. AND MANOCHA, H. L. A Treatise on Generating Functions, Ellis Horwood Limited Publishers, Chichester, Halsted Press, a division of John Wiley and Sons, New York, (1984).        [ Links ]

[10] SRIVASTAVA, H. M. AND KARLSSON, P. W. Multiple Gaussian Hypergeometric Series, John Wiley & Sons (Halsted Press), New York; Ellis Horwood, Chichester, (1985).        [ Links ]

Mumtaz Ahmad Khan
Department of Applied Mathematics
Faculty of Engineering and Technology
Aligarh Muslim University
Aligarh - 202002, U. P
India
e-mail : mumtaz_ahmad_khan_2008@yahoo.com


Bahman Alidad
Department of Mathematics
Faculty of Science
Golestan University
Gorgan
Iran
e-mail : abahman_alidad@yahoo.com

Received : August 2009. Accepted : October 2010