• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.237-253
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• 2010

It is shown that an appropriate combination of methods, relevant to operational calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links with various known polynomials.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.425-447
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• 2020

The family of q-Konhauser matrix polynomials have been extended to Konhauser matrix polynomials. The purpose of the present work is to show that an extension of the explicit forms, generating matrix functions, matrix recurrence relations and Rodrigues-type formula for these matrix polynomials are given, our desired results have been established and their applications are presented.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-438
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• 1996

Let L be a linear functional on the vector space of polynomials in x. Let $\omega(x)$ be a polynomial in x of degree d, for some positive integer d. We consider two sets of polynomials, ${R_n (x)}_{n \geq 0}, {S_n(x)}_{n \geq 0}$, such that $R_n(x)$ is a polynomial in x of degree n and $S_n(x)$ is a polynomial in $\omega(x)$ of degree n. (So $S_n(x)$ is a polynomial in x of degree dn.)

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

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.229-235
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• 2010

In the present paper, we obtain a new formula for the generalized Weyl differintegral operator in a compact form avoiding the occurrence of infinite series and thus making it useful in applications. Our findings provide interesting generalizations and unifications of the results given by several authors and lying scattered in the literature.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1175-1199
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• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.783-797
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• 2013

Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaano$\breve{g}$lu and $\ddot{O}$zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.