• Journal of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1277-1292
• /
• 2009

This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.293-301
• /
• 2022

The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.603-614
• /
• 2012

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. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to present two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. 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 $F^{(m)}_D[{\cdot}]$.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.253-265
• /
• 2012

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. Subse- quently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. 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 ${\varphi}_{n}^{m}(\cdot)$. Here, we aim at defining a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}_{n}^{2}(\cdot)$ and presenting their several generating functions.

• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.373-380
• /
• 2007

In this paper, we derive some generating relations involving Konhauser polynomials, Gauss, Humbert, Appell and Kamp$\acute{e}$ de F$\acute{e}$riet hypergeometric functions with the help of four general theorems on generating functions (partly unilateral and partly bilateral) of one and two variables.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.47-54
• /
• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.473-484
• /
• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.67-79
• /
• 2018

In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.

• Communications of the Korean Mathematical Society
• /
• v.28 no.1
• /
• pp.87-105
• /
• 2013

The aim of the present paper is to study some generating functions of generalized Bateman's and Pasternak's polynomials of two variables.

• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.681-693
• /
• 2024

In this work, we take advantage of Weisnerś group-theoretic and operational identities technique to establish generating functions for the phase-space Hermite polynomials of two-index and two-variables.