# Tagged Questions

Questions on the famed $\zeta(s)$ function of Riemann, and its properties.

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### Behaviour of $\zeta(s)$ near $s=1$

I would appreciate if somebody could run this over and see if it works out? any suggestions or pointers would be appreciated. I denote the standard eta function $\eta$ by $\zeta^{*}$. I have not used ...
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### $\zeta(2n)$ proof [duplicate]

Can anybody pass me on a good source to see the steps in proving, $$\zeta(2n) = \frac{(-1)^{k-1}B_2k (2 \pi)^{2k}}{2(2k)!}$$ I know how we start by looking at the product ...
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### Looking for a way to apply the Taylor Series expansion to find derivatives for a function.

This post references the Riemann-Siegel formula found at here and at here. I am writing a Java program which implements this formula. I am having trouble with the remainder terms. The Riemann-Siegel ...
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### Why is the Bernoulli Number $B_1$ sometimes $+ \frac{1}{2}$?

By using the recursive formula, $$\sum_{i=0}^{n} \binom{n+1}{i} B_i = n+1$$ we find $B_1$ to be $\frac{1}{2}$ and not $- \frac{1}{2}$. Why is this?
I wanted to solve the zeta function for an undefined period "$d$". So for every $d\ge2$. \zeta(-s)= \frac{1}{(d^{s+1}-1)}\sum_{m=1}^{\infty} \frac{1}{2^{m+1}}\sum^{m}_{j=1} (-1)^{j+1}(j)^s\dbinom{m}...