q-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN THREE VARIABLES

- Journal title : Honam Mathematical Journal
- Volume 34, Issue 3, 2012, pp.327-340
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2012.34.3.327

Title & Authors

q-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN THREE VARIABLES

Choi, June-Sang;

Choi, June-Sang;

Abstract

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the -analogue of Gottlieb polynomials. Very recently, Choi defined a -extension of the generalized two variable Gottlieb polynomials and presented their several generating functions. Also, by modifying Khan and Akhlaq`s method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials . Here, in the sequel of the above results for their possible general -extensions in several variables, again, we aim at trying to define a -extension of the generalized three variable Gottlieb polynomials and present their several generating functions.

Keywords

Pochhammer symbol;Generating functions;Generalized hypergeometric function ;(Generalized) Gottlieb polynomials;Lauricella series;a q-analogue of Gottlieb polynomials;q-shifted factorial;q-binomial theorem;Basic (q-) hypergeometric series;

Language

English

Cited by

References

1.

J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), 781-789.

2.

J. Choi, A generalization of Gottlieb polynomials in several variables, Appl. Math. Lett. 25 (2012), 43-46; DOI: 10.1016/j.aml.2011.07.006.

3.

J. Choi, q-Extension of a generalization of Gottlieb polynomials in two variables, J. Chungcheong Math. Soc. 25 (2012), 253-265.

4.

G. Gasper and M. Rahman, Basic Hypergeometric Series (with a Foreword by Richard Askey), Encyclopedia of Mathematics and Its Applications, Vol. 35, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne and Sydney, 1990; Second edition, Encyclopedia of Mathematics and Its Applications, Vol. 96, Cambridge University Press, Cambridge, London and New York, 2004.

5.

M. J. Gottlieb, Concerning some polynomials orthogonal on a nite or enumerable set of points, Amer. J. Math. 60(2) (1938), 453-458.

6.

M. A. Khan and M. Akhlaq, Some new generating functions for Gottlieb polynomials of several variables, Internat. Trans. Appl. Sci. 1(4) (2009), 567-570.

7.

M. A. Khan and M. Asif, A note on generating functions of q-Gottlieb polynomials, Commun. Korean Math. Soc. (2011), Accepted for publication.

8.

G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ. Mat. Palermo 7 (1893), 111-158.

9.

E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.

10.

H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1985.

11.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1984.