Vol. 8, No. 2, 2015
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More explicit formulas for Bernoulli and Euler numbers

Francesca Romano

Vol. 8 (2015), No. 2, 275–284
DOI: 10.2140/involve.2015.8.275
Abstract

By directly considering Taylor coefficients and composite generating functions, we employ a generalized Faà di Bruno formula for higher partial derivatives using vector partitions to obtain identities that include explicit formulas for the Bernoulli and Euler numbers. The formulas we obtain are generalized analogs of the formulas obtained by D. C. Vella.

Keywords
Bernoulli numbers, Euler numbers, multivariable calculus
Mathematical Subject Classification 2010
Primary: 11B68
Secondary: 05A15
Milestones
Received: 3 June 2013
Revised: 4 August 2013
Accepted: 24 September 2013
Published: 3 March 2015

Communicated by Ken Ono
Authors
Francesca Romano
Department of Mathematics
Siena College
Loudonville, NY 12211
United States