__Function:__int**gsl_integration_qawf***(gsl_function **`f`, const double`a`, const double`epsabs`, const size_t`limit`, gsl_integration_workspace *`workspace`, gsl_integration_workspace *`cycle_workspace`, gsl_integration_qawo_table *`wf`, double *`result`, double *`abserr`)-
This function attempts to compute a Fourier integral of the function

`f`over the semi-infinite interval @math{[a,+\infty)}.The parameter @math{\omega} is taken from the table

`wf`(the length`L`can take any value, since it is overridden by this function to a value appropriate for the fourier integration). The integral is computed using the QAWO algorithm over each of the subintervals,where @math{c = (2 floor(|\omega|) + 1) \pi/|\omega|}. The width @math{c} is chosen to cover an odd number of periods so that the contributions from the intervals alternate in sign and are monotonically decreasing when

`f`is positive and monotonically decreasing. The sum of this sequence of contributions is accelerated using the epsilon-algorithm.This function works to an overall absolute tolerance of

`abserr`. The following strategy is used: on each interval @math{C_k} the algorithm tries to achieve the tolerancewhere @math{u_k = (1 - p)p^{k-1}} and @math{p = 9/10}. The sum of the geometric series of contributions from each interval gives an overall tolerance of

`abserr`.If the integration of a subinterval leads to difficulties then the accuracy requirement for subsequent intervals is relaxed,

where @math{E_k} is the estimated error on the interval @math{C_k}.

The subintervals and their results are stored in the memory provided by

`workspace`. The maximum number of subintervals is given by`limit`, which may not exceed the allocated size of the workspace. The integration over each subinterval uses the memory provided by`cycle_workspace`as workspace for the QAWO algorithm.

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