Search Results - generalized hypergeometric functions in several variables

A Class of Generalized Hypergeometric Functions in Several Variables by Yan, Zhimin

“…We study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi…”
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Generalized hypergeometric functions with several variables by Matsubara-Heo, Saiei-Jaeyeong, Oshima, Toshio

“…We introduce a hypergeometric series with several variables, which generalizes Appell’s, Lauricella’s and Kempé de Fériet’s hypergeometric series, and study the system of differential equations that it satisfies…”
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Some New Results for the Kampé de Fériet Function with an Application by Kim, Insuk, Paris, Richard B., Rathie, Arjun K.

“… The theory of generalized hypergeometric functions in several variables comes from the fact that the solutions of the partial differential equations appearing in a large number of applied problems…”
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A class of generalized hypergeometric functions in several variables by Yan, Zhimin

“…We study a class of generalized hypergeometric functions in several variables, $\sb{p}F\sbsp{q}{(d)}$, introduced by A. Koranyi. We prove that $\sb2 F\sbsp{1…”
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Fundamental Solutions of the Generalized Helmholtz Equation with Several Singular Coefficients and Confluent Hypergeometric Functions of Many Variables by Ergashev, T. G.

“… In the theory of hypergeometric functions, an increase in a number of variables will always be accompanied by a complication in the study of the function of several variables…”
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Generalized hypergeometric functions with several variables by Matsubara-Heo, Saiei-Jaeyeong, Oshima, Toshio

“…We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kempé de…”
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Expansions of Kampe de Feriet hypergeometric functions by Komilova, N.J., Hasanov, A., Ergashev, T.G.

“… sum of products of several hypergeometric Gaussian functions, and this in turn facilitates the process of studying the properties of functions in two variables…”
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Notes on Various Implications of Bailey Transformations in Double-Series and Their Consequences by Qureshi, Mohd. Idris, Shah, Tafaz Ul Rahman, Bhat, Aarif Hussain

“…The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications…”
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Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables by Ergashev, Tuhtasin

“… It turns out that all the fundamental solutions of the generalized Helmholtz equation with several singular coefficients are written out through the newly introduced confluent hypergeometric function…”
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On the Volterra-Type Fractional Integro-Differential Equations Pertaining to Special Functions by Singh, Yudhveer, Gill, Vinod, Singh, Jagdev, Kumar, Devendra, Nisar, Kottakkaran Sooppy

“…) involving the generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function in terms of several complex variables in the kernel…”
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CONFLUENT HYPERGEOMETRIC FUNCTIONS OF MANY VARIABLES AND THEIR APPLICATION TO THE FINDING OF FUNDAMENTAL SOLUTIONS OF THE GENERALIZED HELMHOLTZ EQUATION WITH SINGULAR COEFFICIENTS by URINOV, Ahmadzhon Kushakovich, ERGASHEV, Tuhtasin Gulamzhanovich

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Summation Formulas Obtained by Means of the Generalized Chain Rule for Fractional Derivatives by Gaboury, S., Tremblay, R.

“… hypergeometric functions, the Appell F1 function, and the Lauricella functions of several variables FD(n) are given…”
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Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables by Sooppy Nisar, Kottakkaran

“… We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function…”
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Bounds for Incomplete Confluent Fox–Wright Generalized Hypergeometric Functions by Pogány, Tibor K.

“…–Wright functions and/or generalized hypergeometric functions, whilst in the closing part of the article, related bounding inequalities are obtained for them…”
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Some $k$-Horn hypergeometric functions and their properties by Çatak, Caner, Şahin, Recep, Olgun, Ali, Yağcı, Oğuz

“…$-hypergeometric functions. In the light of these studies, we introduce some important recursion formulae for several newly generalized $k…”
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Fractional Calculus Operators and the Mittag-Leffler Function

“… Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest…”
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Hypergeometric Functions of Several Variables and Evaluation of Error Probability in Fading Multichannel System by Brychkov, Yu. A., Savischenko, N. V.

“…) fading and of additive white Gaussian noise (AWGN). This method uses the hypergeometric functions of several variables…”
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Closed-forms of integral transforms in terms of generalized lauricella hypergeometric series: Closed-forms of integral transforms in terms by Belafhal, A., Khannous, F., Usman, T.

“…–Daoust multivariable hypergeometric functions are generalized Lauricella hypergeometric series that are used to express our key findings…”
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Generalized q-difference equations for (q, c)-hypergeometric polynomials and some applications by Cao, Jian, Zhou, Hong-Li, Arjika, Sama

“… ) . Several q -identities such as: generating functions, Andrews–Askey integrals and U ( n + 1 ) type q -binomial formulas for generalized q -polynomials are derived by the method…”
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Appell Hypergeometric Expansions of the Solutions of the General Heun Equation by Ishkhanyan, A. M.

“… equation, we construct several expansions of the solutions of the general Heun equation in terms of Appell generalized hypergeometric functions of two variables of the first kind…”
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