
$$P\left(T\le t:\nu \text{;}\delta \right)={C}_{\nu}\underset{0}{\overset{\infty}{\int}}\left(\frac{1}{\sqrt{2\pi}}\underset{\infty}{\overset{\alpha u\delta}{\int}}{e}^{{x}^{2}/2}dx\right){u}^{\nu 1}{e}^{{u}^{2}/2}du\text{, \hspace{1em}}\nu >0.0$$ 
$${C}_{\nu}=\frac{1}{\Gamma \left(\frac{1}{2}\nu \right){2}^{\left(\nu 2\right)/2}}\text{, \hspace{1em}}\alpha =\frac{t}{\sqrt{\nu}}\text{.}$$ 
(i)  When $t=0.0$, the relationship to the normal is used:


(ii)  Otherwise the series expansion described in Equation 9 of Amos (1964) is used. This involves the sums of confluent hypergeometric functions, the terms of which are computed using recurrence relationships. 
On entry,  ${\mathbf{DF}}<1.0$. 
On entry,  ${\mathbf{MAXIT}}<1$. 
$$F={T}^{2},\lambda ={\delta}^{2},{\nu}_{1}=1\text{\hspace{1em} and \hspace{1em}}{\nu}_{2}=\nu \text{,}$$ 