Saalschütz’ theorem and Rising binomial coefficients – Type 2

A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 142—147
DOI: 10.7546/nntdm.2020.26.2.142-147
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Authors and affiliations

A. G. Shannon
Warrane College, the University of New South Wales
Kensington, NSW 2033, Australia

Abstract

This paper extends some work of Leonard Carlitz on rising binomial coefficients and hypergeometric series in the context of a result of Louis Saalschütz which has animated further work in a number of branches of mathematics as well as physics.

Keywords

  • Gaussian binomial coefficients
  • Rising binomial coefficients – Type 1 and Type 2
  • Hypergeometric series
  • Factorials
  • Difference calculus

2010 Mathematics Subject Classification

  • 33C20
  • 33C05
  • 65B10
  • 33A30
  • 05A30

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Cite this paper

Shannon, A. G. (2020). Saalschütz’ theorem and Rising binomial coefficients – Type 2. Notes on Number Theory and Discrete Mathematics, 26 (2), 142-147, doi: 10.7546/nntdm.2020.26.2.142-147.

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