Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical calculation of the Riemann zeta function at odd integer
  arguments: A direct formula method   In this article, we introduce a recurrence formula which only involves two
adjacent values of the Riemann zeta function at integer arguments. Based on the
formula, an algorithm to evaluate $\zeta$-values(i.e. the values of Riemann
zeta function) at odd-integers from the two nearest $\zeta$-values at
even-integers is posed and proved. The behavior of the error bound is
$O(10^{-n})$ approximately where $n$ is the argument. Our method is especially
powerful for the calculation of Riemann zeta function at large argument, while
for smaller ones it can also reach spectacular accuracies such as more than ten
decimal places.

1
The categories of this paper are: cs
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th