Maxima Function
quad_qaws (f(x), x, a, b, alpha, beta, wfun, epsabs, limit)
quad_qaws(f,x,a,b,alpha,beta,wfun,epsabs,limit)
Integration of w(x) f(x) over a finite interval, where w(x) is a certain algebraic or logarithmic function. A globally adaptive subdivision strategy is applied, with modified Clenshaw-Curtis integration on the subintervals which contain the endpoints of the interval of integration.
quad_qaws
computes the integral using the Quadpack QAWS
routine:
integrate (f(x)*w(x), x, a, b)
The weight function w is selected by wfun:
1
w(x) = (x - a)^alpha (b - x)^beta
2
w(x) = (x - a)^alpha (b - x)^beta log(x - a)
3
w(x) = (x - a)^alpha (b - x)^beta log(b - x)
4
w(x) = (x - a)^alpha (b - x)^beta log(x - a) log(b - x)
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 optional arguments are:
Desired absolute error of approximation. Default is 1d-10.
Size of internal work array. (limit - limlst)/2 is the maximum number of subintervals to use. Default is 200.
epsabs and limit are the desired relative error and the maximum number of subintervals, respectively. epsrel defaults to 1e-8 and limit is 200.
quad_qaws
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;
6
if the input is invalid.
Examples:
(%i1) quad_qaws (1/(x+1+2^(-4)), x, -1, 1, -0.5, -0.5, 1); (%o1) [8.750097361672832, 1.24321522715422E-10, 170, 0] (%i2) integrate ((1-x*x)^(-1/2)/(x+1+2^(-alpha)), x, -1, 1); alpha Is 4 2 - 1 positive, negative, or zero? pos; alpha alpha 2 %pi 2 sqrt(2 2 + 1) (%o2) ------------------------------- alpha 4 2 + 2 (%i3) ev (%, alpha=4, numer); (%o3) 8.750097361672829