Results 21 to 30 of about 3,647,357 (169)

Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]

, 2013
We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Willard Miller Jr., Kalnins, Ernie G., Miller, W., Jr., Miller Jr., W., Sarah Post, Post, Sarah, Post, S., Ernest G. Kalnins, Kalnins, E.G.   +8 more
core   +1 more source

A Bilateral Series Involving Basic Hypergeometric Functions [PDF]

, 2005
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
openaire   +2 more sources

On the bilateral series ψ55 [PDF]

, 2008
The purpose of this paper is to derive two transformation formulae which imply relations between basic and bilateral basic hypergeometric series.
Hu, Qiuxia, Zhang, Zhizheng
core   +1 more source

Transformations and Summations for Bilateral Basic Hypergeometric Series

Arabian Journal of Mathematics
Abstract We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised
Howard S. Cohl, Michael J. Schlosser
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Appell series over finite fields and Gaussian hypergeometric series [PDF]

, 2021
Supervisor: Rupam BarmanIn this thesis we study classical hypergeometric series and Appell series over finite fields, and find finite field analogues of several product and summation formulas satisfied by the classical hypergeometric series ...
Tripathi, Mohit
core  

On digamma series convertible into hypergeometric series [PDF]

, 2023
Series containing the digamma function arise when calculating the parametric derivatives of the hypergeometric functions and play a role in evaluation of Feynman diagrams.
Çetinkaya, Asena, Karp, Dmitrii
core  

New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
doaj   +1 more source

Molecular and Cellular Hallmarks of Age‐Related Vestibular Hair Cell Degeneration

Advanced Science, EarlyView.
This study utilizes single‐cell RNA‐seq transcriptomes, advanced imaging, and electrophysiology to examine universal and cell‐type‐specific aging signatures of vestibular hair cells. The study shows that impaired hair bundle function is a key driver of age‐related vestibular dysfunction.
Samadhi Kulasooriya, Huizhan Liu, Sarath Vijayakumar, Celia Bloom, Zhenhang Xu, Shu Tu, Benjamin J. Borgmeier, Mi Zhou, Litao Tao, Bechara Kachar, David Z. He   +10 more
wiley   +1 more source

Legendre inversions and Ultra-hypergeometric series identities [PDF]

, 2019
In this paper, we extension of hypergeometric series to obtain a new α-hypergeometric series, we establish three terminating Ultra-hypergeometric series identities, by means of Legendre inverse series relations.
Basen, ., Wuyungaowa, ., Basen, Wuyungaowa   +3 more
core   +1 more source

Bilateral Basic Hypergeometric Series: A Study

Anusandhaan - Vigyaan Shodh Patrika, 2018
In the present work, certain transformations and summation formulae for basic bilateral hypergeometric series have been discussed. This study also gives the method of obtaining new transformations and summation formulae for basic bilateral hypergeometric series. Some of the applications have been mentioned.
openaire   +1 more source