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Some supercongruences related to truncated hypergeometric series
In this manuscript, we obtain some supercongruences between truncated classical hypergeometric series using the theory of classic hypergeometric...
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Hypergeometric functions over finite fields
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy...
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Applications of a Hypergeometric Identity and Ramanujan-like Series
The aim of this work is to present an interesting identity relating generalized hypergeometric functions. It allows us to prove many generalizations...
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GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary...
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Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers: More on Integral Representations
AbstractWe consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective...
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Ramanujan and Hypergeometric Series
Ramanujan saw the Gauss summation theorem in Carr’s Synopsis and it remains a mystery till date as to how in one sweep of intuitive imagination he...
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Some identities of certain basic hypergeometric series and their applications to mock theta functions
In this paper, we first obtain the corresponding transformation formulas of the basic bilateral hypergeometric series involving universal mock theta...
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Transformations and Reductions of Srivastava-Daoust Type Double Hypergeometric Functions
The generalized hypergeometric functions of one, two and more variables and allied Special Functions, and their associated transformations,...
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Gauss and the Hypergeometric Equation
Gauss’s work on the hypergeometric equation is described.
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Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series
In 2012, a truncated version for the Euler pentagonal number theorem was established by Andrews and Merca. Since then, a series of papers on the...
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A note on the mean-square solution of the hypergeometric differential equation with uncertainties
The Fröbenius method of power series has been applied to several linear random differential equations. The interest relies on the derivation of a...
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Feynman integrals in two dimensions and single-valued hypergeometric functions
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed...
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The Gauss hypergeometric covariance kernel for modeling second-order stationary random fields in Euclidean spaces: its compact support, properties and spectral representation
This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order...
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Bounds for novel extended beta and hypergeometric functions and related results
We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish...
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Toda and Laguerre–Freud equations and tau functions for hypergeometric discrete multiple orthogonal polynomials
In this paper, the authors investigate the case of discrete multiple orthogonal polynomials with two weights on the step line, which satisfy Pearson...
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A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems
The present study aims to introduce a numerical approach based on the hybrid of block-pulse functions (BPFs), Bernoulli polynomials (BPs), and...
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Acceleration of sequences with transformations involving hypergeometric functions
We introduce a novel class of non-linear transformations of sequences that can accelerate both linear and logarithmic convergence and perform the...
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Solutions of a Confluent Modification of the General Heun Equation in Terms of Generalized Hypergeometric Functions
AbstractWe consider a confluent modification of the general Heun equation having three regular singular points and an irregular singularity of rank...