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.
AbstractIn this paper we obtain explicit formulae for sums of products of a fixed number of consecutive generalized Fibonacci and Lucas numbers. These formulae are related to the recent work of Belbachir and Bencherif. We eliminate all restrictions about the initial values and the form of the recurrence relation. In fact, we consider six different groups of three sums that include alternating sums and sums in which terms are multiplied by binomial coefficients and by natural numbers. The proofs are direct and use the formula for the sum of the geometric series.
AbstractIn the spirit of Euler sums we develop a set of identities for finite sums of products of harmonic numbers in higher order and reciprocal binomial coefficients. The new results complement some Euler sums of the type
AbstractIn this short paper we establish identities involving sums of products of binomial coefficients and coefficients that satisfy the general second–order linear recurrence. We obtain generalizations of identities of Carlitz, Prodinger and Haukkanen.
New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.
Evaluation of sums of products of Gaussianq-binomial coefficients with rationalweight functions