The t-distribution arises in statistics. If Y_1 has a normal distribution and Y_2 has a chi-squared distribution with \nu degrees of freedom then the ratio,
X = { Y_1 \over \sqrt{Y_2 / \nu} }
has a t-distribution t(x;\nu) with \nu degrees of freedom.
p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)} (1 + x^2/\nu)^{-(\nu + 1)/2} dx
for -\infty < x < +\infty.