§24.20 Tables

Abramowitz and Stegun (1964, Chapter 23) includes exact values of $\sum_{k=1}^{m}k^{n}$, $m=1(1)100$, $n=1(1)10$; $\sum_{k=1}^{\infty}k^{-n}$, $\sum_{k=1}^{\infty}(-1)^{k-1}k^{-n}$, $\sum_{k=0}^{\infty}(2k+1)^{-n}$, $n=1,2,\ldots$, 20D; $\sum_{k=0}^{\infty}(-1)^{k}(2k+1)^{-n}$, $n=1,2,\ldots$, 18D.

Wagstaff (1978) gives complete prime factorizations of $N_{n}$ and $\mathop{E_{n}\/}\nolimits$ for $n=20(2)60$ and $n=8(2)42$, respectively. In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, 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).