Extensions of Karlsson–Minton summation theorem and some consequences of the first Miller–Paris transformation

DOI10.1080/10652469.2018.1526793zbMath1402.33008arXiv1806.03434OpenAlexW2963129568WikidataQ129180708 ScholiaQ129180708MaRDI QIDQ4559328

Dmitriĭ Borisovich Karp, Elena G. Prilepkina

Publication date: 3 December 2018

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.03434

zbMATH Keywords

generalized hypergeometric functionhypergeometric summationMiller-Paris transformationKarlsson-Minton summationMeijer-Nørlund function

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (7)

Jacobi-Piñeiro Markov chains ⋮ Hahn multiple orthogonal polynomials of type I: hypergeometric expressions ⋮ Multiple orthogonal polynomials associated with confluent hypergeometric functions ⋮ Alternative Approach to Miller-Paris Transformations and Their Extensions ⋮ Degenerate Miller-Paris transformations ⋮ An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions ⋮ Hypergeometric \({}_4F_3(1)\) with integral parameter differences

Uses Software

• DLMF

Cites Work

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• Transformation formulas for the generalized hypergeometric function with integral parameter differences
• The special functions and their approximations. Vol. I, II
• Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument
• Summation Formulas for Basic Hypergeometric Series
• Partial fractions and bilateral summations
• Generalized Hypergeometric Function of Unit Argument
• Hypergeometric Functions with Integral Parameter Differences
• Special Functions and Orthogonal Polynomials

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