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Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

Article

Abstract

In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of Heine’s transformation, the q-Pfaff–Saalschutz theorem and the q-Kummer sum. Consequently several identities for generalized Fibonomial–Lucanomial coefficients are obtained by specifying the parameter p and the base q.

Keywords

Basic hypergeometric series q-Binomial coefficient Heine transformation q-Pfaff–Saalschutz summation formula q-Kummer sum Fibonomial and Lucanomial coefficients 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhoukou Normal UniversityZhoukouPeople’s Republic of China
  2. 2.Mathematics DepartmentTOBB University of Economics and TechnologySögütözüTurkey
  3. 3.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly

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