Results 21 to 30 of about 9,846 (249)
Some properties of generalized hypergeometric Appell polynomials
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
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Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications
Journal of Inequalities and Applications, 2019 The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings.
Hui Lei +3 more
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Identities for Hypergeometric Integrals of Different Dimensions [PDF]
Letters in Mathematical Physics, 2005 Given complex numbers $m_1,l_1$ and positive integers $m_2,l_2$, such that $m_1+m_2=l_1+l_2$, we define $l_2$-dimensional hypergeometric integrals $I_{a,b}(z;m_1,m_2,l_1,l_2)$, $a,b=0,...,\min(m_2,l_2)$, depending on a complex parameter $z$. We show that $I_{a,b}(z;m_1,m_2,l_1,l_2)=I_{a,b}(z;l_1,l_2,m_1,m_2)$, thus establishing an equality of $l_2$ and
Tarasov, V., Varchenko, A.
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Summation identities and transformations for hypergeometric series [PDF]
Annales mathématiques du Québec, 2017 We find summation identities and transformations for the McCarthy's $p$-adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family $$Z_ : x_1^d+x_2^d=d x_1x_2^{d-1}$$ over a finite field $\mathbb{F}_p$. A.
Barman, Rupam, Saikia, Neelam
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The Askey–Wilson Integral and Extensions
Mathematics, 2023 By means of the q-derivative operator method, we review the q-beta integrals of Askey–Wilson and Nassrallah–Rahman. More integrals are evaluated by the author, making use of Bailey’s identity of well-poised bilateral 6ψ6-series as well as the extended ...
Wenchang Chu
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Hypergeometric series and harmonic number identities
Advances in Applied Mathematics, 2005 10 ...
CHU, Wenchang, DEDONNO L.
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A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials
Revista de Matemática: Teoría y Aplicaciones, 2011 We study a non-standard form of generating function for the three-parameter continuous dual q-Hahn polynomials $p_{n} (x; a, b, | q)$, which has surfaced in a recent work of the present authors on the construction of lifting $q$-difference operators in ...
Mesuma Atakishiyeva, Natig Atakishiyev
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Identities between q-hypergeometric and hypergeometric integrals of different dimensions
Advances in Mathematics, 2005 Preprint (2003), 14 pages, AmsLaTeX, references ...
Tarasov, V., Varchenko, A.
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Bijective proofs of basic hypergeometric series identities [PDF]
Pacific Journal of Mathematics, 1987 The authors give simple, completely bijective proofs of the \(q\)-binomial theorem and Heine's \({}_2\Phi_1\) transformation. Since all identities on basic hypergeometric series can be built out of these two fundamental identities, any basic hypergeometric identity can be proved bijectively, at least in theory, by building bijections out of these ...
Joichi, J. T., Stanton, Dennis
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Differentiation identities for hypergeometric functions
Expositiones Mathematicae, 2022 It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences.
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