Litipk\BigNumbers\Decimal::powerSerie PHP Method

    private static function powerSerie(Decimal $x, Decimal $firstTerm, $scale)
    {
        $approx = $firstTerm;
        $change = InfiniteDecimal::getPositiveInfinite();
        $xPowerN = DecimalConstants::One();
        // Calculates x^n
        $factorN = DecimalConstants::One();
        // Calculates a_n
        $numerator = DecimalConstants::one();
        $denominator = DecimalConstants::one();
        for ($i = 1; !$change->floor($scale + 2)->isZero(); $i++) {
            $xPowerN = $xPowerN->mul($x);
            if ($i % 2 == 0) {
                $factorN = DecimalConstants::zero();
            } elseif ($i == 1) {
                $factorN = DecimalConstants::one();
            } else {
                $incrementNum = Decimal::fromInteger($i - 2);
                $numerator = $numerator->mul($incrementNum, $scale + 2);
                $incrementDen = Decimal::fromInteger($i - 1);
                $increment = Decimal::fromInteger($i);
                $denominator = $denominator->div($incrementNum, $scale + 2)->mul($incrementDen, $scale + 2)->mul($increment, $scale + 2);
                $factorN = $numerator->div($denominator, $scale + 2);
            }
            if (!$factorN->isZero()) {
                $change = $factorN->mul($xPowerN, $scale + 2);
                $approx = $approx->add($change, $scale + 2);
            }
        }
        return $approx->round($scale);
    }