scholarly journals Reducibility of certain Kampé de Fériet function with an application to generating relations for products of two Laguerre polynomials

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 2059-2066
Author(s):  
Junesang Choi ◽  
Arjun Rathie
Keyword(s):  
Special Functions ◽  
Laguerre Polynomials ◽  
Research Subject ◽  
Single Form ◽  
Generating Relations ◽  
Summation Theorem

It has been an interesting and natural research subject to consider the reducibility of some extensively generalized special functions. In this regard, Kamp? de F?riet function has been attracted by many mathematicians. The authors [7] also established many interesting cases of the reducibility of Kamp? de F?riet function by employing generalizations of the two results for the terminating 2F1(2) hypergeometric identities due to Kim et al. In this sequel, we first aim at presenting several interesting cases of the reducibility of Kamp? de F?riet function by using generalizations of classical Kummer?s summation theorem due to Lavoie et al. We next show how one can use the above-given result to obtain eleven new generating relations for products of two Laguerre polynomials in a single-form result. We also consider many interesting and potentially useful specials cases of our main results.

scholarly journals On generalized Lagrange–Hermite–Bernoulli and related polynomials

2020 ◽  
Vol 23 (2) ◽  
pp. 211-224
Author(s):  
Waseem A. Khan ◽  
M. A. Pathan
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Point Of View ◽  
Generalized Polynomials ◽  
New Class ◽  
The Past ◽  
The Family ◽  
Generating Relations ◽  
High Degree

We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials.

scholarly journals Some generating-function equivalences

1975 ◽  
Vol 16 (1) ◽  
pp. 34-39 ◽  
Author(s):  
H. M. Srivastava
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Function ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Classical Orthogonal Polynomials ◽  
Generating Relations ◽  
Sequence Of Functions

A generalization is given of a theorem of F. Brafman [1] on the equivalence of generating relations for a certain sequence of functions. The main result, contained in Theorem 2 below, may be applied to several special functions including the classical orthogonal polynomials such as Hermite, Jacobi (and, of course, Legendre and ultraspherical), and Laguerre polynomials.

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 An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2238
Author(s):  
Rahul Goyal ◽  
Praveen Agarwal ◽  
Alexandra Parmentier ◽  
Clemente Cesarano
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Derivative Operator ◽  
The Family ◽  
Generating Relations ◽  
Fractional Derivative Operators ◽  
Extended Operator ◽  
Two Parameter

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.

scholarly journals Expressions of the Laguerre polynomial and some other special functions in terms of the generalized Meijer $ G $-functions

2021 ◽  
Vol 6 (11) ◽  
pp. 11631-11641
Author(s):  
Syed Ali Haider Shah ◽  
◽  
Shahid Mubeen
Keyword(s):  
Hypergeometric Functions ◽  
Laguerre Polynomial ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Exponential Functions ◽  
Confluent Hypergeometric Functions ◽  
Logarithmic Functions

<abstract><p>In this paper, we investigate the relation of generalized Meijer $ G $-functions with some other special functions. We prove the generalized form of Laguerre polynomials, product of Laguerre polynomials with exponential functions, logarithmic functions in terms of generalized Meijer $ G $-functions. The generalized confluent hypergeometric functions and generalized tricomi confluent hypergeometric functions are also expressed in terms of the generalized Meijer $ G $-functions.</p></abstract>

scholarly journals On partly bilateral and partly unilateral generating functions

1986 ◽  
Vol 28 (2) ◽  
pp. 240-245 ◽  
Author(s):  
M. A. Pathan ◽  
Yasmeen
Keyword(s):  
Generating Functions ◽  
Laguerre Polynomials ◽  
Partial Derivatives ◽  
Starting Point ◽  
Generating Relations

AbstractThe purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.

Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods

2016 ◽  
Vol 23 (3) ◽  
pp. 381-386
Author(s):  
Subuhi Khan ◽  
Rehana Khan
Keyword(s):  
Lie Algebra ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Algebraic Methods ◽  
Generalized Laguerre Polynomials ◽  
Generating Relations

AbstractIn this paper we combine the Lie algebraic methods and the monomiality principle techniques to obtain new results concerning generalized Laguerre polynomials. Also, we derive generating relations involving modified relativistic Laguerre polynomials into the context of the representation ${D(u,m_{0})}$ of a three-dimensional Lie algebra ${\mathrm{sl}(2)}$.

scholarly journals On Applications of Some Special Functions in Statistics

2020 ◽  
Vol 8 (6) ◽  
pp. 1902-1908
Keyword(s):  
Characteristic Function ◽  
Laplace Transform ◽  
Bessel Functions ◽  
Special Functions ◽  
Probability Distributions ◽  
Laguerre Polynomials ◽  
Real Life ◽  
Moment Generating Function ◽  
Cumulative Density Function ◽  
Modified Bessel Functions

In this paper we will introduce some probability distributions with help of some special functions like Gamma, kGamma functions, Beta, k-Beta functions, Bessel, modified Bessel functions and Laguerre polynomials and in mathematical analysis used Laplace transform. We will also obtain their cumulative density function, expected value, variance, Moment generating function and Characteristic function. Some characteristics and real life applications will be computed in tabulated for these distributions

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