scholarly journals A certain sequence of functions involving the Aleph function

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 187-191 ◽  
Author(s):  
P. Agarwal ◽  
M. Chand ◽  
İ. Onur Kiymaz ◽  
A. Çetinkaya
Keyword(s):  
Approximation Theory ◽  
Summation Formulas ◽  
Generating Relations ◽  
Sequence Of Functions

AbstractSequences of functions play an important role in approximation theory. In this paper, we aim to establish a (presumably new) sequence of functions involving the Aleph function by using operational techniques. Some generating relations and finite summation formulas of the sequence presented here are also considered.

scholarly journals A sequence involving an extended Struve function via a differential operator

2021 ◽  
Vol 39 (6) ◽  
pp. 129-137
Author(s):  
Gurmej Singh ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Differential Operator ◽  
Gamma Function ◽  
Summation Formula ◽  
Generating Relations ◽  
Sequence Of Functions

Various extensions of the Struve function have been presented and investigated. Here we aim to introduce an extended Struve function involving the $\mathtt{k}$-gamma function. Then, by using a known differential operator, we introduce a sequence of functions associated with the above introduced extended Struve function and investigate its properties such as generating relations and a finite summation formula. The results presented here, being very general, are also pointed out to yield a number of relatively simple identities.

scholarly journals Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method

2019 ◽  
Author(s):  
Ayman Shehata
Keyword(s):  
Matrix Functions ◽  
Matrix Differential Equation ◽  
Theoretic Method ◽  
Matrix Polynomials ◽  
Summation Formulas ◽  
Group Theoretic Method ◽  
Generating Relations ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Matrix Differential

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

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.

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