## Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

### A simple proof of convolution identities of Bernoulli numbers

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 5 January 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.pja/1420466270

**Digital Object Identifier**

doi:10.3792/pjaa.91.5

**Mathematical Reviews number (MathSciNet)**

MR3296591

**Zentralblatt MATH identifier**

06441200

**Subjects**

Primary: 11B68: Bernoulli and Euler numbers and polynomials

Secondary: 05A19: Combinatorial identities, bijective combinatorics 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

**Keywords**

Bernoulli numbers convolution identity generating function

#### Citation

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. https://projecteuclid.org/euclid.pja/1420466270