Function zeta #
Compute the Riemann Zeta function of a value using an infinite series for all of the complex plane using Riemann’s Functional equation.
Based off the paper by Xavier Gourdon and Pascal Sebah ( http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf )
Implementation and slight modification by Anik Patel
Note: the implementation is accurate up to about 6 digits.
Syntax #
math.zeta(n)
Parameters #
| Parameter | Type | Description |
|---|---|---|
s |
number | Complex | BigNumber | A Real, Complex or BigNumber parameter to the Riemann Zeta Function |
Returns #
| Type | Description |
|---|---|
| number | Complex | BigNumber | The Riemann Zeta of s |
Throws #
Type | Description —- | ———–
Examples #
math.zeta(5) // returns 1.0369277551433895
math.zeta(-0.5) // returns -0.2078862249773449
math.zeta(math.i) // returns 0.0033002236853253153 - 0.4181554491413212i
