Maxima Function
quad_qagi (f(x), x, a, inftype, epsrel, limit)
quad_qagi(f,x,a,inftype,epsrel,limit)
Integration of a general function over an infinite or semi-infinite interval.
The interval is mapped onto a finite interval and
then the same strategy as in quad_qags
is applied.
quad_qagi
evaluates one of the following integrals
integrate (f(x), x, a, inf)
integrate (f(x), x, minf, a)
integrate (f(x), x, minf, inf)
using the Quadpack QAGI routine. The function to be integrated is f(x), with dependent variable x, and the function is to be integrated over an infinite range.
The integrand may be specified as the name of a Maxima or Lisp function or operator, a Maxima lambda expression, or a general Maxima expression.
The parameter inftype determines the integration interval as follows:
inf
The interval is from a to positive infinity.
minf
The interval is from negative infinity to a.
both
The interval is the entire real line.
The optional arguments epsrel and limit are the desired relative error and the maximum number of subintervals, respectively. epsrel defaults to 1e-8 and limit is 200.
quad_qagi
returns a list of four elements:
an approximation to the integral,
the estimated absolute error of the approximation,
the number integrand evaluations,
an error code.
The error code (fourth element of the return value) can have the values:
0
no problems were encountered;
1
too many sub-intervals were done;
2
excessive roundoff error is detected;
3
extremely bad integrand behavior occurs;
4
failed to converge
5
integral is probably divergent or slowly convergent
6
if the input is invalid.
Examples: