2013/11/18 by Christian Lavault, Lavault, Christian
Computer Science · Mathematics · #Advanced Mathematical Identities #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Parallel #Polynomial and algebraic computation #and Cluster Computing (cs.DC) #cs.DC #cs.DM #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1311.4502
15 pages
arxiv created 2013/11/18 · openalex publication_date 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gauß's, the Pfaff-Saalschütz's summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish several dual formulae of Chu-Vandermonde-Gauß's and Pfaff-Saalschütz's summation theorems in Section (3)\citeChuVanGauss and (4)\citePfaffSaalsch, respectively. Finally, the last section is devoted to deriving several identities and reciprocal relations for terminating balanced hypergeometric series from Hagen-Rothe's convolution identity in accordance with the duplicate, triplicate and multiplicate inversions.