Extensions of Karlsson-Minton summation theorem and some consequences of\n the first Miller-Paris transformation

2018/06/09 by Dmitrii Karp, Karp, Dmitrii B., E. G. Prilepkina +1 · 2 citations
Decision Sciences · Mathematics · #33C20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Scientific Measurement and Uncertainty Evaluation

paper · pdf · doi:10.48550/arxiv.1806.03434

openalex publication_date 2018/06/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we give several independent extensions of the Karlsson-Minton\nsummation formula for the generalized hypergeometric function with integral\nparameters differences. In particular, we examine the "prohibited" values for\nthe integer top parameter in Minton's formula, extend one unit negative\ndifference in Karlsson's formula to a finite number of integer negative\ndifferences and establish known and new summation and transformation formulas\nwhen the unit negative difference is allowed to take arbitrary values. We also\npresent a recurrence relation reducing the case of integer negative difference\nto the Karlsson-Minton case of unit negative difference. Further, we explore\nsome alternative forms of the first Miller-Paris transformation, including one\nexpressed in terms of Meijer-Norlund G function.\n

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• Polynomial perturbations of Euler's and Clausen's identities
• Generalized f-Eulerian polynomials: zeros and hypergeometric representations with applications

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