LINEAR RECURSIVE RELATIONS FOR BERNOULLI NUMBERS AND APPLICATIONS

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 114

Abstract

This study concerns a new approach of Bernoulli numbers $B_n$ and Bernoulli numbers $B_n^{(k)}$ of order $k\geq 2$, using properties of some linear recursive relations of infinite order. Linear recursive relations for generating $B_n$ and $B_n^{(k)}$ are established and some identities are provided. Moreover, linear, combinatorial and analytic approaching processes of $B_n$ and $B_n^{(k)}$ are proposed. The closed connection with partial Bell polynomials is considered. Finally, applications to Genocchi numbers $G_n$, Euler numbers $E_n$ and zeta function $\zeta(n)$ are discussed.

Keywords and Phrases

Linear recursive relations of infinite order, $\infty$-generalized Fibonacci sequences, Bernoulli numbers, Combinatorial formula, Approximation processes, Genocchi numbers, Euler numbers, zeta function, partial Bell polynomials.

A.M.S. subject classification

11B83, 11B37, 11B68.

.....

Download PDF 114 Click here to Subscribe now