Results 11 to 20 of about 1,745,713 (225)
AxiomsWe systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided.
Juan Luis González-Santander
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Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which ...
Robin Langer +2 more
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On a new result for the hypergeometric function [PDF]
, 2021 The aim of this note is to provide a new identity connected with the Gauss hypergeometric function.
Paris, Richard B., Rathie, Arjun K.
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A remarkable basic hypergeometric identity. [PDF]
Ramanujan JWe give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.Comment: $1+2+\dots+N = 1\cdot2\dotsb N ...
Krattenthaler C, Zudilin W.
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, 2022 In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role.
Kilicman, Adem +2 more
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The Riemann method for equations with a dominant partial derivative (A Review) [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 This review article is devoted to a class of linear equations with a dominant (leading) partial derivative of the form \((D+M)u=f\), where \(Du\) is a mixed partial derivative, and \(M\) is a linear differential operator containing the derivatives of the
Aleksey N. Mironov +2 more
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Journal of High Energy Physics, 2023 We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on S b 3 / ℤ r $$ {S}_b^3/{\mathbb ...
Ilmar Gahramanov +3 more
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On a hypergeometric identity of Gelfand, Graev and Retakh
, 2003 A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of differential equations, is given hypergeometric proofs.
Rosengren, Hjalmar, +1 more
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Open Physics, 2021 This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized Ψ\Psi -convex and quasi-convex functions.
Chu Yu-Ming +4 more
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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