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Evaluation of sums involving Gaussian $q$ $q$ -binomial coefficients with rational weight functions

Emrah Kiliç

Department of Mathematics, TOBB University of Economics and Technology, 06560 Ankara, Turkey

E-mail Address: ekilic@etu.edu.tr

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and

Helmut Prodinger

Department of Mathematics, University of Stellenbosch, 7602 Stellenbosch, South Africa

E-mail Address: hproding@sun.ac.za

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https://doi.org/10.1142/S1793042116500305Cited by:9 (Source: Crossref)

Abstract

We consider sums of the Gaussian $q$ $q$ -binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications of our results to certain generalized Fibonomial sums weighted with finite products of reciprocal Fibonacci or Lucas numbers.

Keywords:

AMSC: 11B65, 05A30, 11B39

References

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