@stdlib/math-base-special-factorialln

Evaluate the natural logarithm of the factorial function.

Usage no npm install needed!

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README

factorialln

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Natural logarithm of the factorial function.

The natural logarithm of the factorial function may be expressed

Equation of the natural logarithm of the factorial.

The factorial function may be defined as the product

Factorial function definition

or according to the recurrence relation

Factorial function recurrence relation

Following the convention for an empty product, in all definitions,

Zero factorial

The Gamma function extends the factorial function for non-integer values.

Factorial function extension via the Gamma function

The factorial of a negative integer is not defined.

Evaluating the natural logarithm of factorial function is useful as the factorial function can overflow for large n. Thus, factorialln( n ) is generally preferred to ln( n! ).

Installation

npm install @stdlib/math-base-special-factorialln

Usage

var factorialln = require( '@stdlib/math-base-special-factorialln' );

factorialln( x )

Evaluates the natural logarithm of the factorial function. For input values other than negative integers, the function returns ln( x! ) = ln( Γ(x+1) ), where Γ is the Gamma function. For negative integers, the function returns NaN.

var v = factorialln( 3.0 );
// returns ~1.792

v = factorialln( 2.4 );
// returns ~1.092

v = factorialln( -1.0 );
// returns NaN

v = factorialln( -1.5 );
// returns ~1.266

If provided NaN, the function returns NaN.

var v = factorialln( NaN );
// returns NaN

Examples

var incrspace = require( '@stdlib/array-base-incrspace' );
var factorialln = require( '@stdlib/math-base-special-factorialln' );

var x = incrspace( -10.0, 50.0, 0.5 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'x: %d, f(x): %d', x[ i ], factorialln( x[ i ] ) );
}

See Also

Notice

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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License

See LICENSE.

Copyright

Copyright © 2016-2022. The Stdlib Authors.