static RCP<const Basic> diff(const Beta &self,
const RCP<const Symbol> &x) {
RCP<const Basic> beta_arg0 = self.get_args()[0];
RCP<const Basic> beta_arg1 = self.get_args()[1];
RCP<const Basic> diff_beta_arg0 = beta_arg0->diff(x);
RCP<const Basic> diff_beta_arg1 = beta_arg1->diff(x);
return mul(self.rcp_from_this(), add(mul(polygamma(zero, beta_arg0), diff_beta_arg0),
sub(mul(polygamma(zero, beta_arg1), diff_beta_arg1),
mul(polygamma(zero, add(beta_arg0, beta_arg1)), add(diff_beta_arg0, diff_beta_arg1)))));
}
int main()
{
double x;
printf(" x %-22s %-22s %-22s\n",
"psi(x)", "psi'(x)", "psi''(x)");
for (x = -5.5; x <= 0.5; x++)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, psi(x), polygamma(1, x), polygamma(2, x));
for (x = 1; x <= 5; x++)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, psi(x), polygamma(1, x), polygamma(2, x));
for (x = 10; x <= 40; x += 10)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, psi(x), polygamma(1, x), polygamma(2, x));
printf("\n x %-22s %-22s %-22s\n",
"psi3(x)", "psi4(x)", "psi5(x)");
for (x = -5.5; x <= 0.5; x++)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, polygamma(3, x), polygamma(4, x), polygamma(5, x));
for (x = 1; x <= 5; x++)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, polygamma(3, x), polygamma(4, x), polygamma(5, x));
for (x = 10; x <= 40; x += 10)
printf("%4.1f % -22.15g % -22.15g % -22.15g\n",
x, polygamma(3, x), polygamma(4, x), polygamma(5, x));
return EXIT_SUCCESS;
}
static RCP<const Basic> diff(const LogGamma &self,
const RCP<const Symbol> &x) {
RCP<const Basic> arg = self.get_args()[0];
return mul(polygamma(zero, arg), arg->diff(x));
}
static RCP<const Basic> diff(const Gamma &self,
const RCP<const Symbol> &x) {
RCP<const Basic> gamma_arg = self.get_args()[0];
return mul(mul(self.rcp_from_this(), polygamma(zero, gamma_arg)), gamma_arg->diff(x));
}
T polygamma(T z,unsigned m)
{
return polygamma(z,m,boost::math::policies::policy<>());
}
T tgamma_stirl(T z)
{
return polygamma(z,boost::math::policies::policy<>());
}