Generalizations of Jacobsthal sums and hypergeometric series over finite fields
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DOI: 10.1007/s11139-020-00364-w
Abstract: For non-negative integers $$l_{1}, l_{2},\ldots , l_{n}$$ , we define character sums $$\varphi _{(l_{1}, l_{2},\ldots , l_{n})}$$ and $$\psi _{(l_{1}, l_{2},\ldots , l_{n})}$$ over a finite field which are generalizations of Jacobsthal and modified Jacobsthal… read more here.
Keywords: generalizations jacobsthal; hypergeometric series; finite field; series ... See more keywords
Mapping Properties for Convolution Involving Hypergeometric Series
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DOI: 10.1007/s11253-019-01611-0
Abstract: We introduce sufficient conditions for (Gaussian) hypergeometric functions to be in a subclass of analytic functions. In addition, we investigate several mapping properties for convolutions and integral convolutions involving hypergeometric functions. read more here.
Keywords: convolution involving; mapping properties; properties convolution; involving hypergeometric ... See more keywords
Remainder Padé approximants for hypergeometric series
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DOI: 10.1080/10652469.2019.1624542
Abstract: ABSTRACT Remainder Padé Approximation (RPA) consists in adding to the n-th partial sum of a series a suitable Padé approximant of the asymptotic expansion in the variable 1/n of the remainder term. In a previous… read more here.
Keywords: remainder pad; pad approximants; series; hypergeometric series ... See more keywords
Horn's hypergeometric functions with three variables
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DOI: 10.1080/10652469.2020.1814770
Abstract: The work is devoted to obtaining explicit formulas for analytic continuation of quite general hypergeometric series depending on three variables and belonging to the Horn class. We have derived such continuation formulas with respect to… read more here.
Keywords: three variables; hypergeometric functions; continuation; horn hypergeometric ... See more keywords
Values of Gaussian hypergeometric series and their connections to algebraic curves
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DOI: 10.1142/s179304211850001x
Abstract: In this paper, we explicitly evaluate certain special values of 2F1 hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of the number of points on… read more here.
Keywords: values gaussian; series connections; series; algebraic curves ... See more keywords
Certain Derived WP-Bailey Pairs and Transformation Formulas for $q$-Hypergeometric Series
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DOI: 10.2298/fil1714619s
Abstract: In this paper, several results involving the derived WP-Bailey pairs of sequences are established. Furthermore, by using these results, a number of transformation formulas for basic (or $q$-) hypergeometric series are derived. read more here.
Keywords: bailey pairs; derived bailey; hypergeometric series; transformation formulas ... See more keywords
Certain Integral Formulae Associated with the Product of Generalized Hypergeometric Series and Several Elementary Functions Derived from Formulas for the Beta Function
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DOI: 10.3390/sym14020389
Abstract: The literature has an astonishingly large number of integral formulae involving a range of special functions. In this paper, by using three Beta function formulae, we aim to establish three integral formulas whose integrands are… read more here.
Keywords: integral formulae; formulae; hypergeometric series; generalized hypergeometric ... See more keywords
Evaluations of some terminating hypergeometric 2 F 1 (2) series with applications
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DOI: 10.3906/mat-1804-67
Abstract: Explicit expressions for the hypergeometric series 2F1(−n, a; 2a±j; 2) and 2F1(−n, a;−2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer’s second and third summation… read more here.
Keywords: terminating hypergeometric; series applications; evaluations terminating; series ... See more keywords