Riemann Zeta Function numeric computing clarification

Asked Sep 10 '17 at 12:00

Active Sep 10 '17 at 12:00

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I want to implement Riemann Zeta function in some programming language and I try to use algorithms from this question

I have 2 questions:

I cannot find what does it means: $$e_{k}=\sum_{j=k}^{n}\left ( _{a}^{b} \right )$$

most probably it is my lack of math knowledge. Is it well-known polynomial or what?

How to calculate $$\epsilon_{n}(s)$$ if they define it like this $$\left | \epsilon_{n}(s) \right |\leqslant something$$ How can I calculate it? I need exact formula for $$\epsilon_{n}(s) = something$$ I cannot use inequality and I cannot use formula for absolute value for numeric calculations.

asked Sep 10 '17 at 12:00

Zlelik

$$e_{k}=\sum_{j=k}^{n}\left ( _{a}^{b} \right )={b \choose a}+\cdots +{b \choose a},$$ where ${b \choose a}=b!/a!(b-a)!$. – Dietrich Burde Sep 10 '17 at 12:03
I assume $\binom ba$ is a binomial coefficient. – Simply Beautiful Art Sep 10 '17 at 12:03
See this for the correct useful formulas – reuns Sep 10 '17 at 15:27

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