+#include <iostream>
+#include <vector>
+using namespace std;
+
+unsigned tgammaseries(unsigned order)
+{
+ unsigned result = 0;
+ symbol x;
+
+ ex myseries = series(tgamma(x),x==0,order);
+ // compute the last coefficient numerically:
+ ex last_coeff = myseries.coeff(x,order-1).evalf();
+ // compute a bound for that coefficient using a variation of the leading
+ // term in Stirling's formula:
+ ex bound = exp(-.57721566490153286*(order-1))/(order-1);
+ if (abs((last_coeff-pow(-1,order))/bound) > 1) {
+ clog << "The " << order-1
+ << "th order coefficient in the power series expansion of tgamma(0) was erroneously found to be "
+ << last_coeff << ", violating a simple estimate." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned time_gammaseries()