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Closed form evaluation of sums containing squares of Fibonomial coefficients

  • Emrah Kiliç EMAIL logo und Helmut Prodinger
Veröffentlicht/Copyright: 17. August 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 3

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

(Communicated by Stanislav Jakubec)

References

[1] Andrews, G. E.—Askey, R.—Roy, R.: Special Functions, Cambridge University Press, Cambridge, 2000.10.1017/CBO9781107325937Suche in Google Scholar

[2] Gencev, M.: Binomial sums involving harmonic numbers, Math. Slovaca 61 (2011), 215–226.10.2478/s12175-011-0006-5Suche in 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.Suche in 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), 320–329.10.1080/00150517.2011.12428031Suche in Google Scholar

[5] Kiliç, E.—Prodinger, H.: The generalized q-Pilbert matrix, Math. Slovaca 64 (2014), 1083–1092.10.2478/s12175-014-0260-4Suche in 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), 751–770.10.2478/s12175-010-0044-4Suche in Google Scholar

Received: 2012-11-14
Accepted: 2014-1-8
Published Online: 2016-8-17
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0177
Schlagwörter für diesen Artikel
central Fibonomial coefficients; q-analysis; sums identities

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
  29. Research Article
  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
  39. Research Article
  40. A note on Lie product preserving maps on Mn(ℝ)
  41. Research Article
  42. On vector optimality conditions for constrained problems with ℓ-stable data
  43. Research Article
  44. Reparameterization of weakly nonlinear regression models with constraints
  45. Research Article
  46. Convolutions of polynomial kernels
  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
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