It is interesting to note that there are already classical formulas expressing the Bernoulli number
in terms of Stirling numbers such as
Kim, An explicit formula on the generalized Bernoulli number
with order n, Indian J.
j] is the j-th Bernoulli number
, [alpha] > 0 and [beta] > 0 satisfy [alpha][beta] = [[pi].
For the second edition he has corrected errors; clarified some confusion; and added new problems on Bernoulli numbers
, metric spaces, and differential equations.
represent the Bernoulli numbers
1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, .
They included a way to calculate Bernoulli numbers
(a mathematical sequence of numbers) using the machine.
Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers
k](0), k[greater than or equal to]0, the Bernoulli numbers
In just four months, Mohamed Altoumaimi found a formula to explain and simplify the so-called Bernoulli numbers
, a sequence of calculations connected to numbe theory named after the 17th century Swiss mathematician Jacob Bernoulli, the Dagens Nyheter daily said.
Faulhaber was an excellent mathematician, who among other things published the first 16 Bernoulli numbers
in 1631 [18, p.
Stein appeals to graduates, advanced undergraduates and non-specialists in number theory as be describes the modular forms of weights and levels, Dirichlet characters, Eisenstein series and Bernoulli numbers
, dimensions formulas, linear algebra, general modular symbols, computing with newforms, and computing periods.
He'd written a paper about Bernoulli numbers
and I realised that I had noticed some patterns which even he hadn't spotted.