Some Umbral Calculus Presentations of the Chan-Chyan-Srivastava Polynomials and the Erku&amp;#537;-Srivastava Polynomials

The main object of this paper is to present a systematic introduction to the theory and applications of the extended Appell-Lauricella hypergeometric functions defined by means of the extended beta function and extended Dirichlet's beta integral. Their connections with the Laguerre polynomials, the ordinary Lauricella functions and the Srivastava-Daoust generalized Lauricella functions are established for some specific paramters. Furthermore, by applying the various methods and known formulas (such as fractional integral technique; some results of the Lagrange polynomials), we also derive some elegant generating functions for these new functions.

show abstract

“…For other recent results concerning these polynomials and their extensions, we refer to [4], [10] and [29].…”

Section: Generating Functions Formentioning

confidence: 99%

On the extended Appell-Lauricella hypergeometric functions and their applications

Agarwal

Luo

2017

Filomat

View full text Add to dashboard Cite

show abstract

“…On the other hand, Chan-Chyan-Srivastava polynomials, given in [22], have been studied systematically and comprehensively in the literature. For example, q−extension in [1], umbral calculus presentations in [24] and matrix extension in [6] of these multivariable polynomials have been given. Therefore, in the present paper, we construct to q−matrix polynomials in several variables and to derive different families of mixed multilateral and multilinear generating matrix functions for these matrix polynomials.…”

Section: Theorem 13 [18]mentioning

confidence: 99%

Q-matrix polynomials in several variables

Çekіm

2015

Filomat

View full text Add to dashboard Cite

show abstract

“…Liu et al [31] studied various families of bilateral generating functions for the polynomials (1.6). Subsequently, Srivastava et al [32] derived umbral calculus presentations of the polynomials (1.4) and also of the substantially more general polynomials (1.6).…”

Section: Introductionmentioning

confidence: 99%

A q‐Erkuş–Srivastava polynomials operator

Agrawal,

Baxhaku,

Singh

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

Chan et al. (Integral Transforms Spec. Funct. 12 (2), 139–148, (2001)) constructed a multivariable extension of the Lagrange polynomials, popularly known as the Chan–Chyan–Srivastava polynomials. Altin and Erkuş (Integral Transforms Spec. Funct. 17, 239–244, (2006)) proposed Lagrange–Hermite polynomials in several variables. Erkuş and Srivastava (Integral Transforms Spec. Funct., 17, 267–273, (2006)) presented an unification (and generalization) of the Chan–Chyan–Srivastava polynomials and the multivariable Lagrange–Hermite polynomials, called as Erkuş–Srivastava polynomials. Duman (Taiwanese J. Math. 12 (2), 539‐543, (2008)) defined a ‐analogue of these generalized multivariable polynomials. Inspired by these studies, we construct a linear positive operator by means of the ‐Erkuş–Srivastava multivariable polynomials and study the Korovkin‐type theorems and the rate of convergence of these operators by using summability techniques of weighted ‐statistical convergence and the power series method. We also define a th‐order Taylor generalization of the multivariable polynomials operator and investigate the approximation of th‐order continuously differentiable Lipschitz class elements. Finally, we define the bivariate case of ‐Erkuş–Srivastava multivariable polynomials operator and study its ‐statistical convergence by using four‐dimensional matrix transformation.

show abstract

Some Umbral Calculus Presentations of the Chan-Chyan-Srivastava Polynomials and the Erkuș-Srivastava Polynomials

Cited by 9 publications

References 10 publications

On the extended Appell-Lauricella hypergeometric functions and their applications

On the extended Appell-Lauricella hypergeometric functions and their applications

Q-matrix polynomials in several variables

A q‐Erkuş–Srivastava polynomials operator

Contact Info

Product

Resources

About