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 ( )

Implementation and slight modification by Anik Patel

Note: the implementation is accurate up to about 6 digits.

Syntax #


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

See also #


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