Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients



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.


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


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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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