On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences

Abstract

Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, including a reciprocal of polynomial applied to linear higher order recurrences.

On the reciprocal products of generalized Fibonacci sequences

“…For more the nearest integer of the sums of reciprocal of the recurrence sequence studies, see [18][19][20][21]. Specifically, in [19], Trojorský considered finding a sequence that is "asymptotically equivalent" to partial infinite sums and proved that…”

“…Inspired by [19], in this paper, we apply a different research method from the previous one and use the properties of error estimation and the analytic method to study the reciprocal products of {f n }, {l n } and {u n }. We derive some sequences that are asymptotically equivalent to reciprocal products including {f n }, {l n } and {u n }.…”

Reciprocal Formulae among Pell and Lucas Polynomials

“…• Evaluations of reciprocal sums of Pell and Lucas polynomials as well as their extensions (see Wu-Zhang [14] and Trojovský [15]). • Combinatorial interpretations by arranging the Pell numbers on the vertices of polygons (see Celik-Durukan-Özkan [16]) and by counting restricted set partitions (see Mansour and Shattuck [17]).…”