Arabian Journal of Mathematics

, Volume 7, Issue 2, pp 101–112 | Cite as

Evaluation of various partial sums of Gaussian q-binomial sums

  • Emrah Kılıç
Open Access


We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe’s formula and a q-version of the celebrated algorithm of Zeilberger. Finally we give some applications of our results to generalized Fibonomial sums.

Mathematics Subject Classification

11B65 05A30 



  1. 1.
    Calkin, N.J.: A curious binomial identity. Discrete Math. 131, 335–337 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Graham, R.L.; Knuth, D.E.; Patashnik, O.: Concrete Mathematics a Foundation for Computer Science. Addison-Wesley, Boston (1992)zbMATHGoogle Scholar
  3. 3.
    Guo, V.J.W.; Lin, Y.-J.; Liu, Y.; Zhang, C.: A \(q\)-analogue of Zhang’s binomial coefficient identities. Discrete Math. 309, 5913–5919 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    He, B.: Some identities involving the partial sum of \(q\)-binomial coefficients. Electron. J. Comb. 21(3), P3.17 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hirschhorn, M.: Calkin’s binomial identity. Discrete Math. 159, 273–278 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kılıç, E.; Yalçıner, A.: New sums identities in weighted Catalan triangle with the powers of generalized Fibonacci and Lucas numbers. Ars Comb. 115, 391–400 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kılıç, E.; Prodinger, H.: Some Gaussian binomial sum formulæ with applications. Indian J. Pure Appl. Math. 47(3), 399–407 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kılıç, E.; Prodinger, H.: Evaluation of sums involving products of Gaussian \(q\)-binomial coefficients with applications to Fibonomial sums. Turk. J. Math. 41(3), 707–716 (2017)MathSciNetGoogle Scholar
  9. 9.
    Mansour, T.; Shattuck, M.: A \(q\)-analog of the hyperharmonic numbers. Afr. Math. 25, 147–160 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mansour, T.; Shattuck, M.; Song, C.: \(q\)-Analogs of identities involving harmonic numbers and binomial coefficients. Appl. Appl. Math. Int. J. 7(1), 22–36 (2012)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Ollerton, R.L.: Partial row-sums of Pascal’s triangle. Int. J. Math. Educ. Sci. Technol. 38(1), 124–127 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematics DepartmentTOBB Economics and Technology UniversityAnkaraTurkey

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