24 Bernoulli and Euler Polynomials Computation 24.19 Methods of Computation 24.21 Software

§24.20 Tables

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Keywords:: Bernoulli numbers, Euler numbers, sums of powers, tables
Permalink:: http://dlmf.nist.gov/24.20
See also:: Annotations for Ch.24

Abramowitz and Stegun (1964, Chapter 23) includes exact values of $\sum_{k=1}^{m}k^{n}$ , , ; $\sum_{k=1}^{\infty}k^{-n}$ , $\sum_{k=1}^{\infty}(-1)^{k-1}k^{-n}$ , $\sum_{k=0}^{\infty}(2k+1)^{-n}$ , $n=1,2,\dotsc$ , 20D; $\sum_{k=0}^{\infty}(-1)^{k}(2k+1)^{-n}$ , $n=1,2,\dotsc$ , 18D.

Wagstaff (1978) gives complete prime factorizations of $N_{n}$ and $E_{n}$ for and , respectively. In Wagstaff (2002) these results are extended to and , respectively, with further complete and partial factorizations listed up to and , respectively.

For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).

24.19 Methods of Computation 24.21 Software

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