A Comment on Matiyasevich's Identity #0102 with Bernoulli Numbers

Abstract

We connect and generalize Matiyasevich's identity #0102 with Bernoulli numbers and an identity of Candelpergher, Coppo and Delabaere on Ramanujan summation of the divergent series of the infinite sum of the harmonic numbers. The formulae are analytic continuation of Euler sums and lead to new recursion relations for derivatives of Bernoulli numbers. The techniques used are contour integration, generating functions and divergent series.

10 pages

References in corpus (3)

• The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants
• Analytic Continuation of Bernoulli Numbers, a New Formula for the Riemann Zeta Function, and the Phenonmenon of Scattering of Zeros
• Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals