Compute the complete elliptic integral of the second kind.
APACHE-2.0 License
Compute the complete elliptic integral of the second kind.
The complete elliptic integral of the second kind is defined as
E(m)=\int_0^{\pi/2} \sqrt{1 - m (\sin\theta)^2} d\theta
where the parameter m
is related to the modulus k
by m = k^2
.
npm install @stdlib/math-base-special-ellipe
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var ellipe = require( '@stdlib/math-base-special-ellipe' );
Computes the complete elliptic integral of the second kind.
var v = ellipe( 0.5 );
// returns ~1.351
v = ellipe( -1.0 );
// returns ~1.910
v = ellipe( 2.0 );
// returns NaN
v = ellipe( Infinity );
// returns NaN
v = ellipe( -Infinity );
// returns NaN
v = ellipe( NaN );
// returns NaN
-∞ < m <= 1
.var randu = require( '@stdlib/random-base-randu' );
var ellipe = require( '@stdlib/math-base-special-ellipe' );
var m;
var i;
for ( i = 0; i < 100; i++ ) {
m = -1.0 + ( randu() * 2.0 );
console.log( 'ellipe(%d) = %d', m, ellipe( m ) );
}
#include "stdlib/math/base/special/ellipe.h"
Computes the complete elliptic integral of the second kind.
double out = stdlib_base_ellipe( 0.5 );
// returns ~1.351
out = stdlib_base_ellipe( -1.0 );
// returns ~1.910
The function accepts the following arguments:
[in] double
input value.double stdlib_base_ellipe( const double m );
#include "stdlib/math/base/special/ellipe.h"
#include <stdlib.h>
#include <stdio.h>
int main( void ) {
double m;
double v;
int i;
for ( i = 0; i < 100; i++ ) {
m = -1.0 + ( ( (double)rand() / (double)RAND_MAX ) * 2.0 );
v = stdlib_base_ellipe( m );
printf( "ellipe(%lf) = %lf\n", m, v );
}
}
@stdlib/math-base/special/ellipj
: compute the Jacobi elliptic functions sn, cn, and dn.
@stdlib/math-base/special/ellipk
: compute the complete elliptic integral of the first kind.
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
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