Abstract:

Two identities for the Bernoulli and for the Euler numbers are derived. These identities involve two special cases of central combinatorial numbers. The approach is based on a set of differential identities for the powers of the secant. Generalizations of the Mittag-Leffler series for the secant are introduced and used to obtain closed-form expressions for the coefficients.

Keywords: Bernoulli and Euler numbers; powers of the secant function; differential identities

Document Type: Research article

DOI: 10.1080/00207390801935897

Affiliations: 1: Department of Physics, The Royal Military College of Canada, Kingston, ON K7K 7B4, Canada