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Evaluation of sums involving products of Gaussian q-binomial coefficients with applications

  • Emrah Kiliç EMAIL logo and Helmut Prodinger
Published/Copyright: March 18, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 2

Abstract

Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are derived. Then these q-binomial identities will be transformed into Fibonomial sums as consequences.

MSC 2010: Primary 11B39; Secondary 05A30
Keywords: Gaussian q-binomial coefficients; Fibonomial and Lucanomial coefficients; sums identites; partial fraction decomposition

  1. (Communicated by Milan Paštéka)

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Received: 2018-05-11
Accepted: 2018-06-11
Published Online: 2019-03-18
Published in Print: 2019-04-24

© 2019 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0226
Keywords for this article
Gaussian q-binomial coefficients; Fibonomial and Lucanomial coefficients; sums identites; partial fraction decomposition

Articles in the same Issue

  1. Regular papers
  2. RNDr. Miloslav Duchoň, DrSc. passed away ∗ aug. 21, 1932 – †dec. 31, 2018
  3. Prof. RNDr. Gejza Wimmer, DrSc. – A Septuagenerian?
  4. Two monads on the category of graphs
  5. Entropy of MV-algebraic dynamical systems: An example
  6. Going up and lying over in congruence-modular algebras
  7. The minimal arity of near unanimity polymorphisms
  8. On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
  9. The generalized Fermat Conjecture
  10. Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
  11. Integrals of logarithmic functions and alternating multiple zeta values
  12. An abelian subextension of the dyadic division field of a hyperelliptic Jacobian
  13. The class of all semigroups related to semihypergroups of order 2
  14. Criterion for the weak potency of certain HNN extensions
  15. Fekete Szegö theorem for a close-to-convex error function
  16. Bounds for distance between eigenvalues of boundary value problems with retarded argument
  17. Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow
  18. Weak module amenability of triangular banach algebras II
  19. Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class
  20. Example of C-rigid polytopes which are not B-rigid
  21. Some comments on rU-spaces
  22. On the equivalence of various definitions of mixed poisson processes
  23. A note on discrete C-embedded subspaces
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