# Gamma Scaled Lanczos Sum
> Calculate a scaled 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. The scaled Lanczos sum is given by
## Usage
```javascript
var gammaLanczosSumExpGScaled = require( '@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled' );
```
#### gammaLanczosSumExpGScaled( x )
Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function] (scaled by `exp(-g)`, where `g = 10.900511`).
```javascript
var v = gammaLanczosSumExpGScaled( 4.0 );
// returns ~0.018
v = gammaLanczosSumExpGScaled( -1.5 );
// returns ~25.337
v = gammaLanczosSumExpGScaled( -0.5 );
// returns ~-12.911
v = gammaLanczosSumExpGScaled( 0.5 );
// returns ~1.772
v = gammaLanczosSumExpGScaled( 0.0 );
// returns Infinity
v = gammaLanczosSumExpGScaled( NaN );
// returns NaN
```
## Examples
```javascript
var linspace = require( '@stdlib/array/linspace' );
var gammaLanczosSumExpGScaled = require( '@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled' );
var x = linspace( -10.0, 10.0, 100 );
var v;
var i;
for ( i = 0; i < x.length; i++ ) {
v = gammaLanczosSumExpGScaled( x[ i ] );
console.log( 'x: %d, f(x): %d', x[ i ], v );
}
```
[@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
