Results 41 to 50 of about 3,001,317 (197)
Hypergeometric functions in arithmetic geometry [PDF]
, 2009 textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a couple of ways in which hypergeometric functions appear in arithmetic geometry.
Salerno, Adriana Julia, 1979-
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Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Willard Miller Jr. +8 more
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A Feynman integral and its recurrences and associators
Nuclear Physics B, 2016 We determine closed and compact expressions for the ϵ-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations.
Georg Puhlfürst, Stephan Stieberger
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On Some Formulas for the Lauricella Function
Mathematics, 2023 Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables.
Ainur Ryskan, Tuhtasin Ergashev
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Қарағанды университетінің хабаршысы. Математика сериясыHypergeometric functions are divided into complete and confluent functions. Srivastava and Karlsson were the first to propose a method for constructing the complete set of triple Gaussian hypergeometric series and compiled a table containing definitions
A. Hasanov, T.G. Ergashev, A.R. Ryskan
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Mathematics, 2023 The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a
Georgia Irina Oros +1 more
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Precise Estimates for Differences of the Gaussian Hypergeometric Function
Journal of Mathematical Analysis and Applications, 1997 For given \(a,b,c,d\in (0,\infty)\), \(a\leq b\), and \(c< d\), the authors study the problem of comparing the Gaussian hypergeometric functions \(F(a,b; a+b; 1-x^c)\) and \(F(a-\delta, b+\delta; a+b; 1- x^d)\). In particular they solve some open problems by determining \(\sup\{\delta\in (0,\infty): F(a,b; a+b; 1-x^c)< F(a-\delta, b+\delta; a+b; 1-x^d)\
Anderson, G.D, Qiu, S.-L, Vuorinen, M
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Coefficient Conditions for Starlikeness of Nonnegative Order
Abstract and Applied Analysis, 2012 Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z)=∑k=1∞akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit.
Rosihan M. Ali +2 more
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On the complete perturbative solution of one-matrix models
Physics Letters B, 2017 We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear group GL(N ...
A. Mironov, A. Morozov
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Hilbert inequality and Gaussian hypergeometric functions [PDF]
Journal of Mathematical Inequalities, 2009 By using the integral representation of Gaussian hypergeometric function, we obtain Hilbert type inequalities with some fractional kernels and non-conjugate parameters. Such inequalities include the constant factors expressed in terms of hypergeometric functions. Further, we obtain the best possible constants for some general cases, in conjugate case.
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