Mapping integration points and weights
If we have an integral on the form
\begin{equation*}
\int_0^{\infty}f(t)dt,
\end{equation*}
we can choose new mesh points and weights by using the mapping
\begin{equation*}
\tilde{x}_i=tan\left\{\frac{\pi}{4}(1+x_i)\right\},
\end{equation*}
and
\begin{equation*}
\tilde{\omega}_i= \frac{\pi}{4}\frac{\omega_i}{cos^2\left(\frac{\pi}{4}(1+x_i)\right)},
\end{equation*}
where
x_i and
\omega_i are the original mesh points and weights in the
interval
[-1,1] , while
\tilde{x}_i and
\tilde{\omega}_i are the new
mesh points and weights for the interval
[0,\infty) .