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Finite hypergeometric functions [PDF]
Pure and Applied Mathematics Quarterly, 2015 Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on certain l-adic sheafs.
Cohen, Henri, Mellit, Anton, Beukers, F.
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Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions [PDF]
, 2016 25 ...
Holly Swisher +4 more
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DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2011 Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument variable.
Vidunas, Raimundas
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Expansions of Hypergeometric Functions in Hypergeometric Functions [PDF]
Mathematics of Computation, 1961 In [1] Luke gave an expansion of the confluent hypergeometric function in terms of the modified Bessel functions I v ( z ) {I_v}(z) . The existence of other, similar expansions implied that more general expansions might exist. Such was the case.
Jerry L. Fields, Jet Wimp
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Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$
Researches in Mathematics, 2022 Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
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HYPERGEOMETRIC ZETA FUNCTIONS [PDF]
International Journal of Number Theory, 2010 This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers.
Abdul Hassen, Hieu D. Nguyen
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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
Richard L. Coleman, Yudell L. Luke
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A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms
Journal of Mathematics, 2022 The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new.
Vandana Palsaniya +3 more
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AIMS Mathematics, 2021 In this paper, we investigate the relation of generalized Meijer G-functions with some other special functions. We prove the generalized form of Laguerre polynomials, product of Laguerre polynomials with exponential functions, logarithmic functions in ...
Syed Ali Haider Shah, Shahid Mubeen
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Certain subclasses of analytic functions defined by a new general linear operator
Известия Иркутского государственного университета: Серия "Математика", 2018 Hypergeometric functions are of special interests among the complex analysts especially in looking at the properties and criteria of univalent. Hypergeometric functions have been around since 1900’s and have special applications according to their own ...
A.R.S. Juma, M. Darus
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