# Student's t-distribution

## Calculates the probability density function and lower and upper cumulative distribution functions of the student's t-distribution.

percentile x
degree of freedom ν
 ν＞0

density f(x,ν)
lower P(x,ν)
upper Q(x,ν)
 $\normal Student's\ t-distribution\ t(x,\nu)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\nu)={\large\frac{(1+\frac{x^2}{\nu})^{-\frac{\nu+1}{2}}}{\sqrt{\nu}B(\frac{1}{2},\frac{\nu}{2})}}\\(2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\nu)={\large\int_{\small-\infty}^{\hspace{25}\small x}}f(t,\nu)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\nu)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\nu)dt\\$

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