Identities with Bernoulli numbers

found by Yuri Matiyasevich

This HTML paper is written especially for Personal Journal of Yuri MATIYASEVICH.
The paper is updated when new results are found.
Last modified on August 30, 2006.

Notation used
Bernoulli numbers are famous for the numerous identities in which they occur.
I have found some such identities which I believe to be new but I cannot tell it for sure.
If you recognize that an identitiy below has been already published elsewhere, please, inform me.

Most of the identities below have been found with the aid of MATHEMATICA.

Summation indices j, k, l range over positive (even) integers.

Identity #0102

For even m>2
SUMk+l=m (Bk/k)Bl -
SUMk+l=m C(m,k)(Bk/k)Bl -

This identity has related identites, known before, and generalization.

The identity was put on WWW on Feb. 28, 1997.

Identity #0202

For even m>2
(m+2)SUMk+l=m BkBl -
2 SUMk+l=m C(m+2,k)BkBl -
The identity was put on WWW on Feb. 28, 1997.
This identity was generalized by Hao Pan and Zhi-wei Sun in arXiv:math.NT/0407363 to Bernoulli polynomials.
URL of my original Home page is
It has a mirror at

All comments can be e-mailed to me, Yuri Matiyasevich.