Now showing items 1-5 of 5
Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions
(World Scientific Publishing Co. Pte Ltd, 2016-03)
We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ...
Closed Form Evaluation Of Melham's Reciprocal Sums
(Univ Miskolc Inst Math, 2017)
Recently Melham  gives closed formul ae for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we ...
Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
(De Gruyter, 2019-04)
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 ...
Evaluation of sums of products of Gaussian q-binomial coefficients with rational weight functions
Generalizing earlier results, sums over the products of the Gaussian q-binomial coefficients are computed. Some applications of the results for special choices of q are emphasized. The results are obtained by the elementary ...
New reciprocal sums involving finite products of second order recursions
(University of Miskolc, 2019)
In this paper, we present new kinds of reciprocal sums of finite products of general second order linear recurrences. In order to evaluate explicitly them by $q$-calculus, first we convert them into their $q$-notation and ...