# Bernoulli and Euler numbers and polynomials

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##### 1: 24.1 Special Notation
###### BernoulliNumbers and Polynomials
The origin of the notation $B_{n}$, $B_{n}\left(x\right)$, is not clear. …
###### EulerNumbers and Polynomials
Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations $E_{n}$, $E_{n}\left(x\right)$, as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
##### 3: 24.14 Sums
###### §24.14(i) Quadratic Recurrence Relations
24.14.4 $\sum_{k=0}^{n}{n\choose k}E_{k}E_{n-k}=-2^{n+1}E_{n+1}\left(0\right)=-2^{n+2}(% 1-2^{n+2})\frac{B_{n+2}}{n+2}.$
For other sums involving Bernoulli and Euler numbers and polynomials see Hansen (1975, pp. 331–347) and Prudnikov et al. (1990, pp. 383–386).
##### 4: 24.6 Explicit Formulas
24.6.6 $E_{2n}=\sum_{k=1}^{2n}\frac{(-1)^{k}}{2^{k-1}}{2n+1\choose k+1}\*\sum_{j=0}^{% \left\lfloor\tfrac{1}{2}k-\tfrac{1}{2}\right\rfloor}{k\choose j}(k-2j)^{2n}.$
##### 10: 24.19 Methods of Computation
###### §24.19(i) Bernoulli and EulerNumbers and Polynomials
For algorithms for computing $B_{n}$, $E_{n}$, $B_{n}\left(x\right)$, and $E_{n}\left(x\right)$ see Spanier and Oldham (1987, pp. 37, 41, 171, and 179–180). …