Results 11 to 20 of about 278,807 (229)
Value of Generalized Hypergeometric Function at Unity [PDF]
, 1997 Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of $ $-functions.
A. Kazarnovski-Krol
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On the Zeros of Some Generalized Hypergeometric Functions [PDF]
Journal of Mathematical Analysis and Applications, 2000 AbstractLet a1,…,ap,b1,…,bp be real constants with a1,…,ap≠0,−1,−2,… and b1,…,bp>0, and let pFp(z)=pFp(a1,…,ap;b1,…,bp;z). It is shown that the following three conditions are equivalent to each other: (i) pFp(z) has only a finite number of zeros, (ii) pFp(z) has only real zeros, and (iii) the aj's can be re-indexed so that a1=b1+m1,…,ap=bp+mp for some ...
Haseo Ki, Young One Kim
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Contiguity Relations for Generalized Hypergeometric Functions [PDF]
Transactions of the American Mathematical Society, 1995 It is well known that the hypergeometric functions \[ 2 F 1 ( α ± 1 , β , γ ; t ) , 2 F 1
Bernard Dwork, Alan Adolphson
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New Generalized Hypergeometric Functions
Ikonion Journal of Mathematics, 2022 The classical Gauss hypergeometric function and the Kumar confluent hypergeometric function are defined using a classical Pochammer symbol , and a factorial function. This research paper will present a two-parameter Pochhammer symbol, and discuss some of its properties such as recursive formulae and integral representation.
Salım Rabı'u Kabara
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Open Physics, 2022 The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function.
Jain Shilpi +4 more
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Hypergeometric functions as generalized Stieltjes transforms
Journal of Mathematical Analysis and Applications, 2012 16 pages, no ...
Dmitry Karp, E. G. Prilepkina
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Advances in Difference Equations, 2018 In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters.
Ayşegül Çetinkaya +3 more
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Transformation formulas for the generalized hypergeometric function with integral parameter differences [PDF]
, 2013 Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers.
Miller, A. R., Paris, Richard B.
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Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
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Researches in MathematicsThis research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored.
K.K. Chaudhary, S.B. Rao
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