Editing Bernoulli number (section)

=== Recursive definition ===
The Bernoulli numbers obey the sum formulas{{r|Weisstein2016}}
: <math> \begin{align} \sum_{k=0}^{m}\binom {m+1} k B^{-{}}_k &= \delta_{m, 0} \\ \sum_{k=0}^{m}\binom {m+1} k B^{+{}}_k &= m+1 \end{align}</math>
where <math>m=0,1,2...</math> and {{math|''δ''}} denotes the [[Kronecker delta]]. 

The first of these is sometimes written<ref>Jordan (1950) p 233</ref> as the formula (for m > 1)
<math display=block>(B+1)^m-B_m=0,</math>
where the power is expanded formally using the binomial theorem and <math>B^k</math> is replaced by <math>B_k</math>.

Solving for <math>B^{\mp{}}_m</math> gives the recursive formulas<ref>Ireland and Rosen (1990) p 229</ref>
: <math>\begin{align}
  B_m^{-{}} &= \delta_{m, 0} - \sum_{k=0}^{m-1} \binom{m}{k} \frac{B^{-{}}_k}{m - k + 1} \\
  B_m^+ &= 1 - \sum_{k=0}^{m-1} \binom{m}{k} \frac{B^+_k}{m - k + 1}.
\end{align}</math>