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Formulæ related to the \(q\)-Dixon formula with applications to Fibonomial sums

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Abstract

The \(q\)-analogue of Dixon’s identity involves three \(q\)-binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the \(q\)-Dixon formula itself or are “mechanical,” i.e., use the \(q\)-Zeilberger algorithm.

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References

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Acknowledgments

The insightful comments of one referee are gratefully acknowledged.

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Authors and Affiliations

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

    Emrah Kiliç

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

    Helmut Prodinger

Authors
  1. Emrah Kiliç
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  2. Helmut Prodinger
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Correspondence to Emrah Kiliç.

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Kiliç, E., Prodinger, H. Formulæ related to the \(q\)-Dixon formula with applications to Fibonomial sums. Period Math Hung 70, 216–226 (2015). https://doi.org/10.1007/s10998-014-0069-5

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  • DOI: https://doi.org/10.1007/s10998-014-0069-5

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