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Properties and Applications of Extended Hypergeometric Functions
Ingeniería y Ciencia, 2014 In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions.
Daya Krishna Nagar +2 more
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A Connection Formula for the q-Confluent Hypergeometric Function
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show a connection formula for the $q$-confluent hypergeometric functions ${}_2varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2varphi_0(a,b;-;q,x)$, we obtain the connection formula for the $q$-confluent ...
Takeshi Morita
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Fractal and Fractional, 2020 Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol in Diaz et al. 2007, which are one of the vital generalizations of hypergeometric functions.
Övgü Gürel Yılmaz +2 more
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New Zero-Free Regions for Hypergeometric Zeta and Fractional Hypergeometric Zeta Functions
Journal of Mathematics, 2022 We describe and demonstrate zero-free regions for the families called “hypergeometric zeta functions” and “fractional hypergeometric zeta functions”. These zero-free regions are vertical strips in the right half of the complex plane.
Demessie Ergabus Birmechu +1 more
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Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables
Journal of Probability and Statistics, 2020 In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables.
N. J. Hassan +2 more
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Recursion formulas for certain quadruple hypergeometric functions
Advances in Difference Equations, 2021 A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors.
Jihad Younis +4 more
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Some Summation Theorems for Generalized Hypergeometric Functions
Axioms, 2018 Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized
Mohammad Masjed-Jamei, Wolfram Koepf
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Weighted hypergeometric functions and fractional derivative
Advances in Difference Equations, 2017 We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator ...
JE Restrepo +3 more
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International Journal of Mathematics and Mathematical SciencesThis study explores the geometric properties of normalized Gaussian hypergeometric functions in a certain subclass of analytic functions. This work investigates the inclusion properties of integral operators associated with generalized Bessel functions ...
Manas Kumar Giri, Raghavendar K.
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A Generalised Hypergeometric Function [PDF]
Proceedings of the Edinburgh Mathematical Society, 1956 The hypergeometric function1F(a, b; c; z) is analytic in the domain |arg(−z)| < π, and, when |z| < 1, may be represented by the seriesWhen |z| = 1 in the domain |arg(−z)| <π, this series converges2 to F(a; b; c; z) if R(a+b−c) < 0 (integral values of a, b and c are excluded in the present paper).
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