Calculate the Lanczos sum for the approximation of the gamma function.
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> Calculate the Lanczos sum for the approximation of the [gamma function][gamma-function].
The [Lanczos approximation][lanczos-approximation] for the [gamma function][gamma-function] can be written in partial fraction form as follows:
where g is an [arbitrary constant][@stdlib/constants/float64/gamma-lanczos-g] and L_g(n) is the Lanczos sum.
``bash`
npm install @stdlib/math-base-special-gamma-lanczos-sum
`javascript`
var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );
#### gammaLanczosSum( x )
Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].
`javascript
var v = gammaLanczosSum( 4.0 );
// returns ~950.366
v = gammaLanczosSum( -1.5 );
// returns ~1373366.245
v = gammaLanczosSum( -0.5 );
// returns ~-699841.735
v = gammaLanczosSum( 0.5 );
// returns ~96074.186
v = gammaLanczosSum( 0.0 );
// returns Infinity
v = gammaLanczosSum( NaN );
// returns NaN
`
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, -10.0, 10.0, opts );
logEachMap( 'x: %0.4f, f(x): %0.4f', x, gammaLanczosSum );
`
*
`c`
#include "stdlib/math/base/special/gamma_lanczos_sum.h"
#### stdlib_base_gamma_lanczos_sum( x )
Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].
`c
double out = stdlib_base_gamma_lanczos_sum( 4.0 );
// returns ~950.366
out = stdlib_base_gamma_lanczos_sum( -1.5 );
// returns ~1373366.245
`
The function accepts the following arguments:
- x: [in] double input value.
`c`
double stdlib_base_gamma_lanczos_sum( const double x );
`c
#include "stdlib/math/base/special/gamma_lanczos_sum.h"
#include
#include
int main( void ) {
const double x[] = { 4.0, -1.5, -0.5, 0.5 };
double y;
int i;
for ( i = 0; i < 4; i++ ) {
y = stdlib_base_gamma_lanczos_sum( x[ i ] );
printf( "gamma_lanczos_sum(%lf) = %lf\n", x[ i ], y );
}
}
`
*
- [@stdlib/math-base/special/gamma][@stdlib/math/base/special/gamma]: gamma function.
- [@stdlib/math-base/special/gamma-lanczos-sum-expg-scaled][@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled]: calculate a scaled Lanczos sum for the approximation of the gamma function.
*
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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[@stdlib/constants/float64/gamma-lanczos-g]: https://www.npmjs.com/package/@stdlib/constants-float64-gamma-lanczos-g
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[lanczos-approximation]: https://en.wikipedia.org/wiki/Lanczos_approximation
[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma
[@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled