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Expansion of Hypergeometric Functions in Series of Other Hypergeometric Functions [PDF]

Mathematics of Computation, 1961
In a previous paper [1] one of us developed an expansion for the confluent hypergeometric function in series of Bessel functions. A different expansion of the same kind given by Buchholz [2] was also studied. Since publication of [1], it was found that Rice [3] has also developed an expansion of this type, and yet a fourth expansion of this kind can be
Luke, Y. L., Coleman, R. L.
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Some integral properties in the theory of generalized $k-$Bessel matrix functions

Journal of Innovative Applied Mathematics and Computational Sciences
The main purpose of this article is to define some original properties in the theory of the generalized modified $k-$Bessel matrix functions. These special functions, defined in terms of Wright matrix functions, are generalized and their properties ...
Carlo Cattani, Ghazi S. Khammash, Ayman Shehata   +2 more
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Incomplete Caputo fractional derivative operators

Advances in Difference Equations, 2018
The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
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Relations Established Between Hypergeometric Functions and Some Special Number Sequences

Axioms
In this paper, we establish new hypergeometric representations for two classical integer sequences, namely the Pell and Jacobsthal sequences. Motivated by Dilcher’s hypergeometric formulations of the Fibonacci sequence, we extend this framework to other ...
Sukran Uygun, Berna Aksu, Hulya Aytar
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Investigation of Fractional Calculus for Extended Wright Hypergeometric Matrix Functions

Abstract and Applied Analysis, 2023
Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations ...
Mohamed Niyaz, Ahmed H. Soliman, Ahmed Bakhet   +2 more
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A study on unification of generalized hypergeometric function and Mittag-Leffler function with certain integral transforms of generalized basic hypergeometric function

Researches in Mathematics
This research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored.
K.K. Chaudhary, S.B. Rao
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A study of generalized hypergeometric Matrix functions via two-parameter Mittag–Leffler matrix function

Open Physics, 2022
The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function.
Jain Shilpi, Goyal Rahul, Oros Georgia Irina, Agarwal Praveen, Momani Shaher   +4 more
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Hypergeometric Functions for Function Fields

Finite Fields and Their Applications, 1995
Let \(\{a,b,c\}\) be complex constants. Then the famous Gauss hypergeometric equation is given by \[ z(1 - z) {d^2y \over dz^2} + \bigl( c - (a + b + 1) z \bigr) {dy \over dz} - aby = 0. \] One defines the Pochhammer symbol \((a)_n\) by \((a)_0 : = 1\) and for \(n > 1\), \((a)_n : = a(a + 1) (a + 2) (a + 3) \cdots (a + n - 1)\).
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ON CONTIGUITY RELATIONS FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS

Проблемы анализа, 2018
We derive formulas that generalize contiguity relations of Gauss hypergeometric functions to the case of hypergeometric functions satisfying differential equations of arbitrary order and also of solution matrices of their corresponding homogeneous ...
V. A. Gorelov
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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS [PDF]

Honam Mathematical Journal, 2011
Summary: The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas, transform formulas ...
Lee, Dong Myung, Rathie, Arjun K., Parmar, Rakesh K., Kim, Young Sup   +3 more
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