Calculating $\boldsymbol {\lambda _\nu }$

Equation 23 is evaluated numerically to yield a look up table of values for different degrees of freedom. To aid calculation we change the limits as follows

$$\lambda_\nu = \frac{1}{(\nu - 1)(\nu - 2)} \int_{-\infty}^{\infty} \frac{(t^2+\nu-1)^2T_\nu(t)^3}{p(t)^2} dt,$$ (25)

$$w 1/t dt = -w^{-2}dw$$

$$= \frac{2}{(\nu - 1)(\nu - 2)} \left( \int_0^1 \frac{(t^2+\nu-1)^... ...}{p(t)^2}dt + \int_0^1 \frac{({1/w}^2+\nu-1)^2T_\nu(1/w)^3}{p(1/w)^2}dw \right)$$ (26)