## QAGI adaptive integration on infinite intervals

Function: int gsl_integration_qagi (gsl_function * f, double epsabs, double epsrel, size_t limit, gsl_integration_workspace * workspace, double *result, double *abserr)

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.

Function: int gsl_integration_qagiu (gsl_function * f, double a, double epsabs, double epsrel, size_t limit, gsl_integration_workspace * workspace, double *result, double *abserr)

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.

Function: int gsl_integration_qagil (gsl_function * f, double b, double epsabs, double epsrel, size_t limit, gsl_integration_workspace * workspace, double *result, double *abserr)
This function computes the integral of the function f over the semi-infinite interval @math{(-\infty,b)}. The integral is mapped onto the region @math{(0,1]} using the transformation @math{x = b - (1-t)/t},

and then integrated using the QAGS algorithm.