Proceedings of the Japan Academy, Series A, Mathematical Sciences

A simple proof of convolution identities of Bernoulli numbers

Go Yamashita

Full-text: Open access


T. Agoh and K. Dilcher proved convolution identities of Bernoulli numbers in 2007. Their proof was complicated calculations in more than 10 pages, which were based on the relation between the Stirling numbers of second kind and the Bernoulli numbers. In this short paper, we give a simple proof of it. Essentially, the proof is based on just one formula on a new kind of generating function.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 1 (2015), 5-6.

First available in Project Euclid: 5 January 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B68: Bernoulli and Euler numbers and polynomials
Secondary: 05A19: Combinatorial identities, bijective combinatorics 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

Bernoulli numbers convolution identity generating function


Yamashita, Go. A simple proof of convolution identities of Bernoulli numbers. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 1, 5--6. doi:10.3792/pjaa.91.5.

Export citation


  • T. Agoh and K. Dilcher, Convolution identities and lacunary recurrences for Bernoulli numbers, J. Number Theory 124 (2007), no. 1, 105–122.