History of Bernoulli numbers

   comment-sign-convention: Some authors prefer to define $B^+_n = (-1)^n B_n$ as Bernoulli     numbers.+  comment-polynomials: '$B_n = B_n(0)$, the constant term of the $n$-th Bernoulli+    polynomial HREF{Bernoulli_polynomials}. The polynomials are what sums of powers+    are written in: $\sum_{k<m} k^{n} = \frac{B_{n+1}(m) - B_{n+1}}{n+1}$. Their companion+    family, the Euler polynomials HREF{Euler_polynomials}, does the same for alternating+    sums.' Formulas:   formula-cosh: $\sum_{n=0}^\infty \frac{B_nt^n}{n!} =  \frac{t}{2}\left(\coth \frac{t}{2}-1\right)$.