On the product representation of number sequences, with applications to the family of generalized Fibonacci numbers
arXiv:1508.07894 [math.NT], 2015
arXiv:1508.07894 [math.NT], 2015
Abstract
We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the cosine of fractional angles, we then study the special case of the family of $k$-generalized Fibonacci numbers, and present general recursions and identities which link these sequences.