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Bernoulli and Euler numbers and polynomials

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1: 24.1 Special Notation
Bernoulli Numbers and Polynomials
The origin of the notation B n , B n ( x ) , is not clear. …
Euler Numbers 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 ( x ) , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
2: 24.21 Software
§24.21(ii) B n , B n ( x ) , E n , and E n ( x )
3: 24.14 Sums
§24.14 Sums
§24.14(i) Quadratic Recurrence Relations
24.14.4 k = 0 n ( n k ) E k E n - k = - 2 n + 1 E n + 1 ( 0 ) = - 2 n + 2 ( 1 - 2 n + 2 ) 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 2 n = k = 1 2 n ( - 1 ) k 2 k - 1 ( 2 n + 1 k + 1 ) j = 0 1 2 k - 1 2 ( k j ) ( k - 2 j ) 2 n .
5: 24.5 Recurrence Relations
§24.5 Recurrence Relations
6: 24.2 Definitions and Generating Functions
§24.2 Definitions and Generating Functions
§24.2(i) Bernoulli Numbers and Polynomials
§24.2(ii) Euler Numbers and Polynomials
§24.2(iii) Periodic Bernoulli and Euler Functions
Table 24.2.1: Bernoulli and Euler numbers.
n B n E n
7: 24.9 Inequalities
§24.9 Inequalities
8: 24.11 Asymptotic Approximations
24.11.4 ( - 1 ) n E 2 n 8 n π ( 4 n π e ) 2 n .
9: 17.3 q -Elementary and q -Special Functions
§17.3(iii) Bernoulli Polynomials; Euler and Stirling Numbers
10: 24.19 Methods of Computation
§24.19(i) Bernoulli and Euler Numbers and Polynomials
For algorithms for computing B n , E n , B n ( x ) , and E n ( x ) see Spanier and Oldham (1987, pp. 37, 41, 171, and 179–180). …