# Riemann Zeta Function
> [Riemann zeta][zeta-function] function.
The [Riemann zeta][zeta-function] function is the [analytic continuation][analytic-continuation] of the infinite series
where `s` is a complex variable equal to `σ + ti`. The series is only convergent when the real part of `s`, `σ`, is greater than `1`.
## Usage
```javascript
var zeta = require( '@stdlib/math/base/special/riemann-zeta' );
```
#### zeta( s )
Evaluates the [Riemann zeta][zeta-function] function as a function of a real variable `s` (i.e., `t = 0`).
```javascript
var v = zeta( 1.1 );
// returns ~10.584
v = zeta( -4.0 );
// returns 0.0
v = zeta( 70.0 );
// returns 1.0
v = zeta( 0.5 );
// returns ~-1.46
v = zeta( 1.0 ); // pole
// returns NaN
v = zeta( NaN );
// returns NaN
```
## Examples
```javascript
var linspace = require( '@stdlib/array/linspace' );
var zeta = require( '@stdlib/math/base/special/riemann-zeta' );
var s;
var v;
var i;
s = linspace( -50.0, 50.0, 200 );
for ( i = 0; i < s.length; i++ ) {
v = zeta( s[ i ] );
console.log( 's: %d, ζ(s): %d', s[ i ], v );
}
```
[zeta-function]: https://en.wikipedia.org/wiki/Riemann_zeta_function
[analytic-continuation]: https://en.wikipedia.org/wiki/Analytic_continuation
