Results 21 to 30 of about 60,471 (199)

Logarithmic A-hypergeometric series [PDF]

International Journal of Mathematics, 2020
The method of Frobenius is a standard technique to construct series solutions of an ordinary linear differential equation around a regular singular point. In the classical case, when the roots of the indicial polynomial are separated by an integer, logarithmic solutions can be constructed by means of perturbation of a root.
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Certain Properties Associated with Generalized $M$-Series using Hadamard Product [PDF]

Sahand Communications in Mathematical Analysis
The generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function.  The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and ...
Dheerandra Sachan, Dinesh Kumar, Kottakkaran Nisar   +2 more
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Decomposition formulas for some quadruple hypergeometric series

Қарағанды университетінің хабаршысы. Математика сериясы, 2020
In the present work, the authors obtained operator identities and decomposition formulas for second order Gauss hypergeometric series of four variables into products containing simpler hypergeometric functions. A Choi–Hasanov method based on the inverse
A.S. Berdyshev, A. Hasanov, A.R. Ryskan
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Hypergeometric evaluation identities and supercongruences [PDF]

, 2010
In this article, we provide an application of hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series.
Long, Ling
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Hypergeometric series

Japanese journal of mathematics. New series, 1993
This paper explains how to get integral representations for general hypergeometric series in one or several variables. The way is first to construct the so-called ``exponential modules'' lengthily studied in the \textit{B. Dwork's} book [Generalized hypergeometric functions (Oxford Press 1990; Zbl 0747.33001)] then to use a formal Laplace transform ...
Dwork, B., Loeser, F.
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Recurrent identities for two special functions of hypergeometric type

Вестник Самарского университета: Естественнонаучная серия, 2023
The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation [PDF]

, 2014
We consider a $q$-Painlev\'e IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them
Nakazono, Nobutaka
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Infinite families of accelerated series for some classical constants by the Markov-WZ Method [PDF]

Discrete Mathematics & Theoretical Computer Science, 2005
In this article we show the Markov-WZ Method in action as it finds rapidly converging series representations for a given hypergeometric series. We demonstrate the method by finding new representations for log(2),ζ(2) and ζ(3).
Mohamud Mohammed
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Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients

Journal of Function Spaces, 2022
The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into ...
B. R. Srivatsa Kumar, Adem Kılıçman, Arjun K. Rathie   +2 more
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Landen inequalities for special functions [PDF]

, 2013
In this paper our aim is to present some Landen inequalities for Gaussian hypergeometric functions, confluent hypergeometric functions, generalized Bessel functions and for general power series.
Baricz, Árpád
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