The problem is that your are trying to use the exlusive-or operator ^ to perform exponentiation **.

This works:

use Math::Trig;
use bignum;
sub factorial
{
  my $n = @_;
  my $root = sqrt($n*2*pi);
  my $exp = ($n/exp(1)) ** $n;
  my $result =$root*$exp;
  return $result;
}

my $b = 2032597;
my $r = Math::BigInt->new(factorial($b));
print "b is $b\n";
print "the calculated result is $r\n";
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