Results 61 to 70 of about 821 (208)
Some $k$-Horn hypergeometric functions and their properties
Journal of New Results in Science, 2023 In the theory of special functions, the $k$-Pochhammer symbol is a generalization of the Pochhammer symbol. With the help of the $k$-Pochhammer symbol, we introduce and study a new generalization of the $k$-Horn hypergeometric functions such as, ${G}_{1}^
Caner Çatak +3 more
doaj +1 more source
Small Structures, Volume 7, Issue 2, February 2026.This work describes how to conceive validated mixed machine learned/empirical energy functions based on finite‐sized molecular clusters for condensed phase simulations. Energy functions for pure and heterogeneous systems are one of the backbones for molecular simulation of condensed phase systems.
JingChun Wang +10 more
wiley +1 more source
Some Properties of Extended Hypergeometric Function and Its Transformations
, 2018 There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent ...
Prakriti Rai, Aparna Chaturvedi
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Hypergeometric motives from Euler integral representations
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We revisit certain one‐parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of L$L$‐series attached to nondegenerate ...
Tyler L. Kelly, John Voight
wiley +1 more source
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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Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.This article focuses on the study of fractional integral operators involving the H―‐function. Two main theorems are established that present new fractional integral formulas associated with the H―‐function. Moreover, several well‐known results related to various special functions can be derived as particular cases by assigning suitable parameter values
S. Chandak +3 more
wiley +1 more source
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.In this study, we introduce the two‐parameter Pochhammer matrix function. Notably, we establish the (p, k) Pochhammer matrix symbol as a key new construct for our generalizations. Furthermore, we construct gamma and beta matrix functions of two parameters and prove properties similar to their classical counterparts.
Mohamed S. Al–Sheikh +4 more
wiley +1 more source
MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION
Проблемы анализа, 2017 The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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A Review of Certain Modern Special Functions and Their Applications
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed +2 more
wiley +1 more source
Some New Hypergeometric Transformations via Fractional Calculus Technique [PDF]
, 2020 In this paper, we establish a new hypergeometric transformation involving Gauss function using fractional calculus technique. We also obtain some other known and new identities involving Gauss function as special cases of our main result.
Faisal Khan, Mohammad
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