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

**Full paper (PDF, 98 Kb)**

## Details

### 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.