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Natural logarithm of the factorial function.
The natural logarithm of the factorial function may be expressed
The factorial function may be defined as the product
or according to the recurrence relation
Following the convention for an empty product, in all definitions,
The Gamma function extends the factorial function for non-integer values.
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! ).
To use in Observable,
factorialln = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-factorialln@umd/browser.js' )To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:
var factorialln = require( 'path/to/vendor/umd/math-base-special-factorialln/index.js' )To include the bundle in a webpage,
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-factorialln@umd/browser.js"></script>If no recognized module system is present, access bundle contents via the global scope:
<script type="text/javascript">
(function () {
window.factorialln;
})();
</script>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 ~1.266If provided NaN, the function returns NaN.
var v = factorialln( NaN );
// returns NaN<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/array-base-incrspace@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-factorialln@umd/browser.js"></script>
<script type="text/javascript">
(function () {
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 ] ) );
}
})();
</script>
</body>
</html>@stdlib/math-base/special/factorial: evaluate a factorial.
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.
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