Table of the Student t Distribution

The table above gives approximate quantiles of the Student \(t\) distribution with \(n\) degrees of freedom:

\[ F^{-1}(p) \text{ where } F(t) = \int_{-\infty}^t \frac{\Gamma[(n + 1) / 2]}{\sqrt{n\,\pi} \Gamma(n / 2)} \left(1 + \frac{x^2}{n}\right)^{-(n+1)/2} dx \]