public void BernoulliNumbers()
{
Assert.IsTrue(AdvancedIntegerMath.BernoulliNumber(0) == 1.0);
Assert.IsTrue(AdvancedIntegerMath.BernoulliNumber(1) == -1.0 / 2.0);
Assert.IsTrue(AdvancedIntegerMath.BernoulliNumber(2) == 1.0 / 6.0);
Assert.IsTrue(AdvancedIntegerMath.BernoulliNumber(3) == 0.0);
Assert.IsTrue(AdvancedIntegerMath.BernoulliNumber(4) == -1.0 / 30.0);
}
//[TestMethod]
// Cancellation too bad to be useful
public void BernoulliStirlingRelationship()
{
// This involves significant cancellation, so don't pick n too high
foreach (int n in TestUtilities.GenerateIntegerValues(2, 16, 4))
{
double S = 0.0;
for (int k = 0; k <= n; k++)
{
double dS = AdvancedIntegerMath.Factorial(k) / (k + 1) * AdvancedIntegerMath.StirlingNumber2(n, k);
if (k % 2 != 0)
{
dS = -dS;
}
S += dS;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(S, AdvancedIntegerMath.BernoulliNumber(n)));
}
}
/// <inheritdoc />
public override double Cumulant(int r)
{
if (r < 0)
{
throw new ArgumentOutOfRangeException("r");
}
else if (r == 0)
{
return(0.0);
}
else if (r == 1)
{
return(Mean);
}
else if (r % 2 != 0)
{
return(0.0);
}
else
{
return(AdvancedIntegerMath.BernoulliNumber(r) / r * (MoreMath.Pow(n, r) - 1.0));
}
}
/// <inheritdoc />
public override double Cumulant(int r)
{
if (r < 0)
{
throw new ArgumentOutOfRangeException(nameof(r));
}
else if (r == 0)
{
return(0.0);
}
else if (r == 1)
{
return(range.Midpoint);
}
else if (r % 2 != 0)
{
// This isn't strictly necessary since BernoulliNumber(r) will return 0, but there is no reason to compute (b-a)^r
return(0.0);
}
else
{
return(MoreMath.Pow(range.Width, r) * AdvancedIntegerMath.BernoulliNumber(r) / r);
}
}