Re: [HM] Bernoulli Numbers

Michael Lambrou (LAMBROU@talos.cc.uch.gr)
Tue, 6 Jul 1999 11:57:51 +0300 (MET-DST)

Recently the LIST had a query concerning the Staudt-Clausen formula for
Bernoulli numbers.
A more general result (with a not so difficult proof) can be found in L.
Carlitz, A note on Bernoulli numbers of higher order, Scripta Mathematica
22 (1956) 217-221.

In passing let me mention that a formula for the sum of k to the power p
(for k=1 to n-1) using Bernoulli numbers is included in G. Carr, Formulas
and Theorems, paragraph 2939 (the book Ramanujan loved, and reprinted by
Chelsea Publications). The reason I mention is because Carr has a misprint
there: the n on line 4 of paragraph 2939 should be a p.

Michael Lambrou
Department of Mathematics
University of Crete
Iraklion 71409
Greece

e-mail: LAMBROU@TALOS.CC.UCH.GR