# ゼータ関数 Zeta Function
# 引数 次数 変数 ($N, $X)
# 戻り値 ゼータ関数 ($ZetaFunction)
sub ZETAFUNCTION{
	my ($X) = @_;
	my $ZetaFunction = 0;
	my $Zeta = 0;
	my $PrevZeta = 0;
	my $BinomialCoefficient = 0;
	my $Sum = 0;
	my $Sign = 0;
	my $Limit = 100;
	my $Epsilon = 1.0e-10;
	
	# 値の確認
	if($X == 1){
		return 0;
	}
	
	# 計算
	for(my $i = 0; $i < $Limit; $i++){
		$Sum = 1 ** (-$X);
		$BinomialCoefficient = 1;
	
		for(my $j = 1; $j <= $i; $j++){
			# 符号
			$Sign = (($j % 2) == 0 ? 1 : -1);
			# 二項係数 Binomial Coefficient
			$BinomialCoefficient = $BinomialCoefficient * (($i - ($j - 1)) / $j);
	
			$Sum += ($Sign * $BinomialCoefficient * (($j + 1) ** (-$X)));
		}
	
		# 一つ前
		$PrevZeta = $Zeta;
		$Zeta += ((2 ** (-($i + 1))) * $Sum);
	
		# 収束判定
		last if(abs($Zeta - $PrevZeta) < $Epsilon);
	}
	
	# ゼータ関数 Zeta Function
	$ZetaFunction = (1 / (1 - (2 ** (1 - $X)))) * $Zeta;
	
	return $ZetaFunction;
}