Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

Some Trigonometric Identities Involving Fibonacci and Lucas Numbers

In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √

Fibonacci numbers and trigonometric identities

Webb & Parberry proved in 1969 a startling trigonometric identity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.

A symmetric algorithm for hyperharmonic and Fibonacci numbers

In this work, we introduce a symmetric algorithm obtained by the recurrence relation an = a k n−1+a k−1 n . We point out that this algorithm can be apply to hyperharmonic-, ordinary and incomplete Fibonacciand Lucas numbers. An explicit formulae for hyperharmonic numbers, general generating functions of the Fibonacciand Lucas numbers are obtained. Besides we define ”hyperfibonacci numbers”, ”hy...

Generalizations of Some Identities Involving the Fibonacci Numbers

Some Identities for Fibonacci and Incomplete Fibonacci p-Numbers via the Symmetric Matrix Method

We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.