Identity #0102 with Bernoulli numbers


This WWW page is a part of an HTML paper from Personal Journal of Yuri MATIYASEVICH.
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 -
(m+1)Bm=0
Identity #0102
(found by Yuri Matiyasevich):
SUMk+l=m (Bk/k)Bl -
SUMk+l=m C(m,k)(Bk/k)Bl -
BmHm=0
Miki's identity:
SUMk+l=m (Bk/k)(Bl/l) -
SUMk+l=m C(m,k)(Bk/k)(Bl/l) -
2(Bm/m)Hm=0
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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