2.6 KiB
2.6 KiB
Riemann Zeta Function
Riemann zeta function.
The Riemann zeta function is the 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
var zeta = require( '@stdlib/math/base/special/riemann-zeta' );
zeta( s )
Evaluates the Riemann zeta function as a function of a real variable s
(i.e., t = 0
).
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
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 );
}