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

Choi, June-Sang

  • Received : 2012.04.24
  • Accepted : 2012.05.22
  • Published : 2012.09.25

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 $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ 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 ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.

Keywords

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

References

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Cited by

  1. FORMULAS DEDUCIBLE FROM A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES vol.34, pp.4, 2012, https://doi.org/10.5831/HMJ.2012.34.4.603