Hypergeometric differential equation and new identities for the coefficients of Nørlund and Bühring

DOI10.3842/SIGMA.2016.052zbMath1342.33013arXiv1602.07375OpenAlexW2286781136MaRDI QIDQ298877

Dmitriĭ Borisovich Karp, Elena G. Prilepkina

Publication date: 21 June 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07375

zbMATH Keywords

generalized hypergeometric functionBernoulli polynomialsMeijer's \(G\)-functionhypergeometric differential equationBühring's coefficientsNørlund's coefficients

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (11)

Some new facts concerning the delta neutral case of Fox's \(H\) function ⋮ On Meijer's G function G^m,n_p,p for m + n = p ⋮ Extensions of Karlsson–Minton summation theorem and some consequences of the first Miller–Paris transformation ⋮ Hypergeometric functions at unit argument: simple derivation of old and new identities ⋮ Trigonometric identities: from Hermite via Meijer, Nørlund, and Braaksma to Chu and Johnson and beyond ⋮ Further applications of the \(G\) function integral method ⋮ Alternative Approach to Miller-Paris Transformations and Their Extensions ⋮ Representations of hypergeometric functions for arbitrary parameter values and their use ⋮ Generalized Volterra functions, its integral representations and applications to the Mathieu-type series ⋮ Uniformly convergent expansions for the generalized hypergeometric functions _p–1F_p and _pF_p ⋮ An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions

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