The (f,g)-inversion formula and its applications: the (f,g)-summation formula

2005/05/03 by Xinrong Ma, Ma, Xinrong
Mathematics · #05A10 #33C20 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10 #msc:33C20

paper · pdf · doi:10.48550/arxiv.math/0505042

33 pages

arxiv created 2005/06/21 · arxiv updated 2009/12/01

Abstract

A complete characterization of two functions f(x,y) and g(x,y) in the (f,g)-inversion is presented. As an application to the theory of hypergeometric series, a general bibasic summation formula determined by f(x,y) and g(x,y) as well as four arbitrary sequences is obtained which unifies Gasper and Rahman's, Chu's and Macdonald's bibasic summation formula. Furthermore, an alternative proof of the (f,g)-inversion derived from the (f,g)-summation formula is presented. A bilateral (f,g)-inversion containing Schlosser's bilateral matrix inversion as a special case is also obtained.

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