Title: Inversion techniques and reciprocal formulae

Authors: Chuanan Wei; Dianxuan Gong

Addresses: Department of Information Technology, Hainan Medical College, Haikou City, Hainan Province 571101, China. ' College of Sciences, Hebei United University, Tangshan City 063009, Hebei Province, China

Abstract: Combinatorics has an important role in the development of computer science. Combinatorial identity which attracts numerous mathematicians is absolutely an important branch of it. As the effective tools, all kinds of inversion techniques are often used to prove known results and find new identities. In this paper, we shall employ Gould-Hsu inversions and Carlitz inversions to establish several pairs of interesting reciprocal formulae. Meanwhile, 15 three-term transformations for ₂φ₁− series and the corresponding hypergeometric forms are offered.

Keywords: binomial theorem; Gould–Hsu inversions; Rothy's identity; Carlitz inversions; reciprocal formulae; combinatorics; combinatorial identity; hypergeometric forms.

DOI: 10.1504/IJCAT.2012.046042

International Journal of Computer Applications in Technology, 2012 Vol.43 No.2, pp.117 - 127

Published online: 27 Mar 2012 *

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