This function computes the integral of the function f over the infinite interval @math{(-\infty,+\infty)}. The integral is mapped onto the interval @math{(0,1]} using the transformation @math{x = (1-t)/t},
It is then integrated using the QAGS algorithm. The normal 21-point Gauss-Kronrod rule of QAGS is replaced by a 15-point rule, because the transformation can generate an integrable singularity at the origin. In this case a lower-order rule is more efficient.
This function computes the integral of the function f over the semi-infinite interval @math{(a,+\infty)}. The integral is mapped onto the interval @math{(0,1]} using the transformation @math{x = a + (1-t)/t},
and then integrated using the QAGS algorithm.
and then integrated using the QAGS algorithm.