Results 61 to 70 of about 5,448,308 (166)
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
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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
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Some Contiguous Relation on k-Generalised Hypergeometric Function [PDF]
, 2020 In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”.
Kumari, Sona, Joshi, Sunil, Mittal, Ekta
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Degenerate Gauss hypergeometric functions
, 2007 In this paper we study terminating and ill-defined Gauss hypergeometric functions. For their hypergeometric equations, the set of 24 Kummer′s solutions degenerates. We describe those solutions and relations between them.Kyushu University 21st Century COE
Vidunas, Raimundas
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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
Functional reduction of one-loop Feynman integrals with arbitrary masses
Journal of High Energy Physics, 2022 A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail. The method is based on a repeated application of the functional relations proposed by the author.
O. V. Tarasov
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Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F 1
Journal of High Energy PhysicsIn celestial conformal field theory (CCFT), the 4d massless scalars are represented by 2d conformal operators with conformal dimensions h = h ¯ $$ \overline{h} $$ = (1 + iλ)/2.
Wei Fan
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Abstract and Applied Analysis, 2014 Computing the matrix elements of the linear operator, which transforms the spherical basis of SO(3,1)-representation space into the hyperbolic basis, very recently, Shilin and Choi (2013) presented an integral formula involving the product of two ...
I. A. Shilin, Junesang Choi
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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
, 2021 Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science.
Muajebah Hidan, Mohamed Abdalla
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