spence
Spence's function, also known as the dilogarithm.
The dilogarithm is defined as
or also alternatively as
Usage
var spence = require( '@stdlib/math/base/special/spence' );
spence( x )
Evaluates Spence's function, which is alternatively known as the dilogarithm.
var v = spence( 3.0 );
// returns ~-1.437
v = spence( 0.0 );
// returns ~1.645
v = spence( NaN );
// returns NaN
For negative numbers, the dilogarithm is not defined.
var v = spence( -4.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var spence = require( '@stdlib/math/base/special/spence' );
var x;
var i;
for ( i = 0; i < 100; i++ ) {
x = randu() * 100.0;
console.log( 'spence( %d ) = %d', x, spence( x ) );
}
C APIs
Usage
#include "stdlib/math/base/special/spence.h"
stdlib_base_spence( x )
Evaluates Spence's function, which is alternatively known as the dilogarithm.
double out = stdlib_base_spence( 3.0 );
// returns ~-1.437
out = stdlib_base_spence( 0.0 );
// returns ~1.645
The function accepts the following arguments:
- x:
[in] double
input value.
double stdlib_base_spence( const double x );
Examples
#include "stdlib/math/base/special/spence.h"
#include <stdio.h>
int main( void ) {
const double x[] = { 3.0, 9.0, 0.0, -10.0 };
double y;
int i;
for ( i = 0; i < 4; i++ ) {
y = stdlib_base_spence( x[ i ] );
printf( "spence(%lf) = %lf\n", x[ i ], y );
}
}