# Riemann Zeta Function at Odd Integers

## Unsolved Problem

The value of the Riemann $\zeta$ function for odd integers has not been determined.

For certain values it has been calculated to whatever number of places, but an exact expression has never been found.

## Examples

### Riemann Zeta Function of $3$

Apéry's constant is the value of the infinite sum:

$\map \zeta 3 = \displaystyle \sum_{n \mathop = 1}^\infty \frac 1 {n^3}$

where $\zeta$ denotes the Riemann zeta function.

Its approximate value is given by:

$\map \zeta 3 \approx 1 \cdotp 20205 \, 69031 \, 59594 \, 28539 \, 97381 \, 61511 \, 44999 \, 07649 \, 86292 \ldots$