| public static lowerIncompleteGamma ( $s, $x ) : number | ||
| $s | ||
| $x | ||
| Результат | number | |
public static function lowerIncompleteGamma($s, $x)
{
if ($s == 1) {
return 1 - exp(-1 * $x);
}
if ($s == 0.5) {
$√π = sqrt(\M_PI);
$√x = sqrt($x);
return $√π * self::erf($√x);
}
if (round($s * 2, 0) == $s * 2) {
return ($s - 1) * self::lowerIncompleteGamma($s - 1, $x) - $x ** ($s - 1) * exp(-1 * $x);
}
$tol = 1.0E-12;
$xˢ∕s∕eˣ = $x ** $s / exp($x) / $s;
$sum = 1;
$fractions = [];
$element = 1 + $tol;
while ($element > $tol) {
$fractions[] = $x / ++$s;
$element = array_product($fractions);
$sum += $element;
}
return $xˢ∕s∕eˣ * $sum;
}