Identity #0102 with Bernoulli numbers

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Last modification done on August 30, 2006.

Notation used
This identity can be viewed as an "interpolation" between two identities known before. Namely, for even m>2 we have:

Euler identity:

-SUMk+l=m C(m,k)BkBl -
Identity #0102
(found by Yuri Matiyasevich):
SUMk+l=m (Bk/k)Bl -
SUMk+l=m C(m,k)(Bk/k)Bl -
Miki's identity:
SUMk+l=m (Bk/k)(Bl/l) -
SUMk+l=m C(m,k)(Bk/k)(Bl/l) -
The latter identity was found by Hiroo Miki in A relation between Bernoulli numbers, J. of Number Theory, vol. 10 (1978), no. 3, pp. 297-302; MR: 80a:10024.

Another proof and generalizations of Miki's identity were given in the following works:

Identity #0102 was later proved and generalized in the following works:

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