static void Faulhaber(int p)
{
Console.Write("{0} : ", p);
Frac q = new Frac(1, p + 1);
int sign = -1;
for (int j = 0; j <= p; j++)
{
sign *= -1;
Frac coeff = q * new Frac(sign, 1) * new Frac(Binomial(p + 1, j), 1) * Bernoulli(j);
if (Frac.ZERO == coeff)
{
continue;
}
if (j == 0)
{
if (Frac.ONE != coeff)
{
if (-Frac.ONE == coeff)
{
Console.Write("-");
}
else
{
Console.Write(coeff);
}
}
}
else
{
if (Frac.ONE == coeff)
{
Console.Write(" + ");
}
else if (-Frac.ONE == coeff)
{
Console.Write(" - ");
}
else if (Frac.ZERO < coeff)
{
Console.Write(" + {0}", coeff);
}
else
{
Console.Write(" - {0}", -coeff);
}
}
int pwr = p + 1 - j;
if (pwr > 1)
{
Console.Write("n^{0}", pwr);
}
else
{
Console.Write("n");
}
}
Console.WriteLine();
}
static Frac Bernoulli(int n)
{
if (n < 0)
{
throw new ArgumentException("n may not be negative or zero");
}
Frac[] a = new Frac[n + 1];
for (int m = 0; m <= n; m++)
{
a[m] = new Frac(1, m + 1);
for (int j = m; j >= 1; j--)
{
a[j - 1] = (a[j - 1] - a[j]) * new Frac(j, 1);
}
}
// returns 'first' Bernoulli number
if (n != 1)
{
return(a[0]);
}
return(-a[0]);
}