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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

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1337-2211
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Volume 66, Issue 3

Issues

Closed form evaluation of sums containing squares of Fibonomial coefficients

Emrah Kiliç / Helmut Prodinger
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0177

Abstract

We give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms of a variable q, and then to use generating functions and Rothe's identity from classical q-calculus.

MSC 2010: Primary 11B39

Keywords: central Fibonomial coefficients; q-analysis; sums identities

References

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    Andrews, G. E.—Askey, R.—Roy, R.: Special Functions, Cambridge University Press, Cambridge, 2000.Google Scholar

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    Gencev, M.: Binomial sums involving harmonic numbers, Math. Slovaca 61 (2011), 215–226.Google Scholar

  • [3]

    Kiliç, E.—Ohtsuka, H.—Akkus, I.: Some generalized Fibonomial sums related with the Gaussian q-binomial sums, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), 51–61.Google Scholar

  • [4]

    Kiliç, E.—Prodinger, H.—Akkus, I.—Ohtsuka, H.: Formulas for Fibonomial sums with generalized Fibonacci and Lucas coefficients, Fibonacci Quart. 49 (2011), 320–329.Google Scholar

  • [5]

    Kiliç, E.—Prodinger, H.: The generalized q-Pilbert matrix, Math. Slovaca 64 (2014), 1083–1092.Google Scholar

  • [6]

    Pražaќ, P.—Trojovský, P.: On sums related to the numerator of generating functions for the kth power of Fibonacci numbers, Math. Slovaca 60 (2010), 751–770.Google Scholar

About the article


Received: 2012-11-14

Accepted: 2014-01-08

Published Online: 2016-08-17

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 757–767, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0177.

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[2]
Emrah Kiliç and Ilker Akkus
Mathematica Slovaca, 2018, Volume 68, Number 3, Page 501

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