Compute the inverse hyperbolic cotangent.
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> Compute the [inverse hyperbolic cotangent][hyperbolic-arctangent] of a double-precision floating-point number.
``bash`
npm install @stdlib/math-base-special-acoth
`javascript`
var acoth = require( '@stdlib/math-base-special-acoth' );
#### acoth( x )
Computes the [inverse hyperbolic cotangent][hyperbolic-arctangent] of a double-precision floating-point number.
`javascript
var v = acoth( 2.0 );
// returns ~0.5493
v = acoth( 1.0 );
// returns Infinity
`
The domain of the inverse hyperbolic cotangent is the union of the intervals (-inf,-1] and [1,inf). If provided a value on the open interval (-1,1), the function returns NaN.
`javascript
var v = acoth( 0.0 );
// returns NaN
v = acoth( 0.5 );
// returns NaN
`
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var acoth = require( '@stdlib/math-base-special-acoth' );
var x = uniform( 100, 1.0, 5.0, {
'dtype': 'float64'
});
logEachMap( 'acoth(%0.4f) = %0.4f', x, acoth );
`
*
`c`
#include "stdlib/math/base/special/acoth.h"
#### stdlib_base_acoth( x )
Computes the [inverse hyperbolic cotangent][hyperbolic-arctangent] of a double-precision floating-point number.
`c`
double out = stdlib_base_acoth( 2.0 );
// returns ~0.5493
The function accepts the following arguments:
- x: [in] double input value.
`c`
double stdlib_base_acoth( const double x );
`c
#include "stdlib/math/base/special/acoth.h"
#include
int main( void ) {
const double x[] = { 1.0, 1.44, 1.89, 2.33, 2.78, 3.22, 3.67, 4.11, 4.56, 5.0 };
double v;
int i;
for ( i = 0; i < 10; i++ ) {
v = stdlib_base_acoth( x[ i ] );
printf( "acoth(%lf) = %lf\n", x[ i ], v );
}
}
`
*
- [@stdlib/math-base/special/acosh][@stdlib/math/base/special/acosh]: compute the hyperbolic arccosine of a double-precision floating-point number.
- [@stdlib/math-base/special/acot][@stdlib/math/base/special/acot]: compute the inverse cotangent.
- [@stdlib/math-base/special/asinh][@stdlib/math/base/special/asinh]: compute the hyperbolic arcsine of a double-precision floating-point number.
- [@stdlib/math-base/special/atanh][@stdlib/math/base/special/atanh]: compute the hyperbolic arctangent of a double-precision floating-point number.
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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---
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Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
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[deno-url]: https://github.com/stdlib-js/math-base-special-acoth/tree/deno
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[umd-url]: https://github.com/stdlib-js/math-base-special-acoth/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-acoth/blob/umd/README.md
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[esm-readme]: https://github.com/stdlib-js/math-base-special-acoth/blob/esm/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-acoth/main/LICENSE
[hyperbolic-arctangent]: https://en.wikipedia.org/wiki/Inverse_hyperbolic_function
[@stdlib/math/base/special/acosh]: https://www.npmjs.com/package/@stdlib/math-base-special-acosh
[@stdlib/math/base/special/acot]: https://www.npmjs.com/package/@stdlib/math-base-special-acot
[@stdlib/math/base/special/asinh]: https://www.npmjs.com/package/@stdlib/math-base-special-asinh
[@stdlib/math/base/special/atanh]: https://www.npmjs.com/package/@stdlib/math-base-special-atanh