Results 81 to 90 of about 43,514 (215)
A new proof of Watson's theorem for the series 3F2(1) [PDF]
, 2009 We give a new proof of the classical Watson theorem for the summation of a 3F2 hypergeometric series of unit argument.
Paris, R. B., Rathie, Arjun K.
core
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
Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function [PDF]
, 2010 Through Alday-Gaiotto-Tachikawa conjecture, we show how triality observed in N = 2 SU(2) N f = 4 QCD can be interpreted geometrically as the interplay among six of Kummer's 24 solutions belonging to one fixed Riemann scheme in the context of ...
Ta-Sheng Tai
semanticscholar +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
doaj +1 more source
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
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
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
doaj +1 more source
Composition Formula for Saigo Fractional Calculus Operator on p R q Function
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we use the Saigo operators to create fractional integral and derivative formulations involving the generalized p R q function. The resulting expressions are represented using generalized Wright hypergeometric functions. We develop various results for fractional integrals and derivatives of the Weyl, Erdélyi–Kober, Saigo, and Riemann ...
Belete Debalkie +2 more
wiley +1 more source
Expressions for values of the gamma function
, 2004 This paper presents expressions for gamma values at rational points with the denominator dividing 24 or 60. These gamma values are expressed in terms of 10 distinct gamma values and rational powers of $\pi$ and a few real algebraic numbers.
Vidunas, Raimundas
core +1 more source
Study of (p, q)‐Symmetric Starlike Functions of Order η
Journal of Function Spaces, Volume 2026, Issue 1, 2026.In the field of geometric function theory, we use the (p, q)‐differential operator in the complex unit disk to describe a novel class Sp,q∗∗η of symmetrical starlike functions of order η. Several interesting properties of functions belonging to the class Sp,q∗∗η are examined, such as growth, distortion, and convolution characteristics.
Imran Khan +4 more
wiley +1 more source