Riemann Zeta Function at Odd Integers/Examples

Examples of Riemann Zeta Function at Odd Integers

Riemann Zeta Function of $3$

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

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

where $\zeta$ denotes the Riemann zeta function.

Its approximate value is given by:

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