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Tagged with binomial-coefficients riemann-zeta-function
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What is known about sums of the form $\sum_{n=2}^{\infty}[\zeta(n)-1]^{p} $?
A fair bit is known about rational zeta series. This includes identities like $$ \sum_{n=2}^{\infty} [\zeta(n) -1] = 1 . $$
Many more identities can be found in articles by e.g. Borwein and Adamchik &...
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Show that the ratio of limits converges to the nearest Riemann zeta zero except when the ratio is a singularity
Let $h(s,n)$ be:
$$h(s,n)=\lim_{c\to 1} \, \frac{(-1)^{n-2}}{(n-2)!}\zeta (c)^{n-2} \sum _{k=1}^{n-1} \frac{(-1)^{k-1} \binom{n-2}{k-1}}{\zeta ((c-1) (k-1)+s)}$$
and let $g(s,n)$ be:
$$g(s,n)=\lim_{c\...
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