FORMULAS DEDUCIBLE FROM A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 4,  2012, pp.603-614
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.4.603
Title & Authors
FORMULAS DEDUCIBLE FROM A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES
Choi, Junesang;

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 $\small{q}$-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $\small{m}$ variables to present two generating functions of the generalized Gottlieb polynomials $\small{{\varphi}^m_n({\cdot})}$. Here, we show that many formulas regarding the Gottlieb polynomials in m variables and their reducible cases can easily be obtained by using one of two generating functions for Choi's generalization of the Gottlieb polynomials in m variables expressed in terms of well-developed Lauricella series $\small{F^{(m)}_D[{\cdot}]}$.
Keywords
Pochhammer symbol;Generating functions;Generalized hypergeometric function $\small{_pF_q}$;(Generalized) Gottlieb polynomials;Lauricella series;
Language
English
Cited by
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