scholarly journals Polynomials of the Laguerre type

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 261-267
Author(s):  
Gospava Djordjevic
Keyword(s):  
Real Number ◽  
Hypergeometric Function ◽  
Generating Function ◽  
Laguerre Polynomials ◽  
Explicit Representation ◽  
Convolution Type ◽  
Generalized Laguerre Polynomials ◽  
Special Cases

In this noteweshall study a class of polynomials {f c,r n,m(x)}, where c is some real number, r ? N?{0}, m ? N. These polynomials are defined by the generating function. Also, for these polynomials we find an explicit representation in the form of the hypergeometric function; some identities of the convolution type are presented; some special cases are shown. The special cases of these polynomials are: Panda?s polynomials [2], [4]; the generalized Laguerre polynomials [1], [6]; the Celine Fasenmyer polynomials [3].

scholarly journals Two variables generalized Laguerre polynomials

2021 ◽  
Vol 13 (1) ◽  
pp. 134-141
Author(s):  
A. Asad
Keyword(s):  
Differential Equations ◽  
Hypergeometric Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Laguerre Polynomial ◽  
Laguerre Polynomials ◽  
Explicit Representation ◽  
Generalized Hypergeometric Function ◽  
Generalized Laguerre Polynomials

The objective of this paper is to introduce and study the generalized Laguerre polynomial for two variables. We prove that these polynomials are characterized by the generalized hypergeometric function. An explicit representation, generating functions and some recurrence relations are shown. Moreover, these polynomials appear as solutions of some differential equations.

scholarly journals Some generating functions and properties of extended second Appell function

2017 ◽  
Vol 37 (1) ◽  
pp. 169-176
Author(s):  
Rakesh K. Parmar ◽  
Sunil Dutt Purohit
Keyword(s):  
Hypergeometric Function ◽  
Generating Function ◽  
Generating Functions ◽  
Laguerre Polynomials ◽  
Special Cases ◽  
Differentiation Formulas ◽  
Appell Function ◽  
Number Of Authors

Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing (presumably new) a generating function for the extended second Appell hypergeometric function $F_{2} (a, b, b'; c, c'; x, y; p)$. Further we derive a relation in terms of the Laguerre polynomials and differentiation formulas. We also present special cases of the main results of this paper.

scholarly journals Some bilateral generating functions involving the Erkus-Srivastava polynomials and some general classes of multivariable polynomials

2014 ◽  
Vol 45 (4) ◽  
pp. 341-356 ◽  
Author(s):  
Sébastien Gaboury ◽  
Richard Tremblay ◽  
Mehmet Ali Özarslan
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Computer Modelling ◽  
Laguerre Polynomials ◽  
Contour Integral ◽  
Special Cases ◽  
Biorthogonal Polynomials ◽  
Lauricella Function ◽  
Bilateral Generating Functions ◽  
Fox’S H Function

Recently, Liu et al. [Bilateral generating functions for the Erkucs-Srivastava polynomials and the generalized Lauricella function, Appl.Math.Comput.218 (2012),pp.7685-7693 investigated some various families of bilateral generating functions involving the Erkucs Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Erkucs-Srivastava 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), pp.1-6, A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J.Math.117 (1985), pp.183-191] and by Kaanouglu and Ozarslan in Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), pp.625-631. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.

scholarly journals Extended elliptic-type integrals with associated properties and Turán-type inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rakesh K. Parmar ◽  
Ritu Agarwal ◽  
Naveen Kumar ◽  
S. D. Purohit
Keyword(s):  
Hypergeometric Function ◽  
Laguerre Polynomials ◽  
Beta Function ◽  
Gauss Hypergeometric Function ◽  
Elliptic Type ◽  
Integral Formulas ◽  
Special Cases ◽  
Turán Type Inequalities ◽  
Extended Beta Function ◽  
Function Of Two Variables

AbstractOur aim is to study and investigate the family of $(p, q)$ ( p , q ) -extended (incomplete and complete) elliptic-type integrals for which the usual properties and representations of various known results of the (classical) elliptic integrals are extended in a simple manner. This family of elliptic-type integrals involves a number of special cases and has a connection with $(p, q)$ ( p , q ) -extended Gauss’ hypergeometric function and $(p, q)$ ( p , q ) -extended Appell’s double hypergeometric function $F_{1}$ F 1 . Turán-type inequalities including log-convexity properties are proved for these $(p, q)$ ( p , q ) -extended complete elliptic-type integrals. Further, we establish various Mellin transform formulas and obtain certain infinite series representations containing Laguerre polynomials. We also obtain some relationship between these $(p, q)$ ( p , q ) -extended elliptic-type integrals and Meijer G-function of two variables. Moreover, we obtain several connections with $(p, q)$ ( p , q ) -extended beta function as special values and deduce numerous differential and integral formulas. In conclusion, we introduce $(p, q)$ ( p , q ) -extension of the Epstein–Hubbell (E-H) elliptic-type integral.

scholarly journals Properties and Applications of a New Extended Gamma Function Involving Confluent Hypergeometric Function

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Abdus Saboor ◽  
Gauhar Rahman ◽  
Hazrat Ali ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Hypergeometric Function ◽  
Generating Function ◽  
Gamma Function ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Pochhammer Symbol ◽  
Special Cases ◽  
Derivative Formulas

In this paper, a new confluent hypergeometric gamma function and an associated confluent hypergeometric Pochhammer symbol are introduced. We discuss some properties, for instance, their different integral representations, derivative formulas, and generating function relations. Different special cases are also considered.

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

Sign in / Sign up

Export Citation Format

Share Document