private static function F($x, int $ν, $μ)
{
Support::checkLimits(self::LIMITS, ['x' => $x, 'ν' => $ν, 'μ' => $μ]);
$Φ = StandardNormal::CDF(-$μ);
$y = $x ** 2 / ($x ** 2 + $ν);
$sum = $Φ;
$tol = 1.0E-8;
$j = 0;
do {
$exp = exp(-1 * $μ ** 2 / 2) * ($μ ** 2 / 2) ** $j;
$pⱼ = 1 / Combinatorics::factorial($j) * $exp;
$qⱼ = $μ / sqrt(2) / Special::gamma($j + 3 / 2) * $exp;
$I1 = Special::regularizedIncompleteBeta($y, $j + 1 / 2, $ν / 2);
$I2 = Special::regularizedIncompleteBeta($y, $j + 1, $ν / 2);
$delta = $pⱼ * $I1 + $qⱼ * $I2;
$sum += $delta / 2;
$j += 1;
} while ($delta / $sum > $tol || $j < 10);
return $sum;
}