f(q;k,\nu)=\frac{\sqrt{2\pi}k(k-1)\nu^{\nu/2}}{\Gamma\left(\frac \nu 2 \right)2^{\nu/2-1}}\int_0^\infty x^\nu \varphi(\sqrt\nu x)\left[\int_{-\infty}^\infty \varphi(u)\varphi(u-qx) (\Phi(u)-\Phi(u-qx))^{k-2} \, \text{d}u\right] \, \text{d}x .
When the degrees of freedom approach infinity, the standard normal distribution can be used for the general equation above.