A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125037
Abstract: We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as the cases… read more here.
Keywords: generalized hypergeometric; confluent heun; confluent; general single ... See more keywords
Parameter derivatives of the generalized hypergeometric function
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DOI: 10.1080/10652469.2017.1362635
Abstract: ABSTRACT In this paper, the parameter derivatives to any order of the generalized hypergeometric function as well as for its various special cases are obtained. read more here.
Keywords: hypergeometric function; generalized hypergeometric; parameter derivatives; derivatives generalized ... See more keywords
Generalized hypergeometric distribution and its applications on univalent functions
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DOI: 10.1186/s13660-020-02515-5
Abstract: The purpose of the present paper is to introduce a generalized hypergeometric distribution and obtain some necessary and sufficient conditions for generalized hypergeometric distribution series belonging to certain classes of univalent functions associated with the… read more here.
Keywords: generalized hypergeometric; univalent functions; applications univalent; distribution applications ... See more keywords
An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions
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DOI: 10.1515/fca-2018-0071
Abstract: Abstract In this paper we investigate the extension of the multiple Erdélyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by the way of regularization. The regularization involves derivatives of the function… read more here.
Keywords: multiple erd; generalized hypergeometric; lyi kober; erd lyi ... See more keywords
Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions
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DOI: 10.3390/axioms10040310
Abstract: The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and… read more here.
Keywords: function; continued fraction; branched continued; generalized hypergeometric ... See more keywords
Some Summation Theorems for Generalized Hypergeometric Functions
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DOI: 10.3390/axioms7020038
Abstract: 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… read more here.
Keywords: summation; generalized hypergeometric; hypergeometric functions; theorems generalized ... 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
Some New Results for the Kampé de Fériet Function with an Application
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DOI: 10.3390/sym14122588
Abstract: The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications. The theory of generalized hypergeometric functions in several variables comes from the fact that… read more here.
Keywords: function; generalized hypergeometric; hypergeometric functions; kamp riet ... See more keywords