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The Maxima on-line user's manual

Algebra Calculator

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Quad_qawf Calculator

Quad_qawf

Function: quad_qawf (<f(x)>, <x>, <a>, <omega>, <trig>, [<epsabs>, <limit>, <maxp1>, <limlst>])

Function: quad_qawf (<f>, <x>, <a>, <omega>, <trig>, [<epsabs>, <limit>, <maxp1>, <limlst>]) Calculates a Fourier cosine or Fourier sine transform on a semi-infinite interval using the Quadpack QAWF function. The same approach as in quad_qawo is applied on successive finite intervals, and convergence acceleration by means of the Epsilon algorithm (Wynn, 1956) is applied to the series of the integral contributions.

quad_qawf computes the integral

integrate (f(x)*w(x), x, a, inf)

The weight function w is selected by <trig>:

cos w(x) = cos (omega x)

sin w(x) = sin (omega 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 keyword arguments are optional and may be specified in any order. They all take the form key=val. The keyword arguments are:

<epsabs> Desired absolute error of approximation. Default is 1d-10.

<limit> Size of internal work array. (<limit> - <limlst>)/2 is the maximum number of subintervals to use. Default is 200.

<maxp1> Maximum number of Chebyshev moments. Must be greater than 0. Default is 100.

<limlst> Upper bound on the number of cycles. Must be greater than or equal to 3. Default is 10.

quad_qawf 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_qawf (exp(-x^2), x, 0, 1, cos, epsabs=1d-9);
          (%o1)   [.6901942235215714, 2.84846300257552E-11, 215, 0]
          (%i2) integrate (exp(-x^2)*cos(x), x, 0, inf);
                                    - 1/4
                                  %e      sqrt(%pi)
          (%o2)                   -----------------
                                          2
          (%i3) ev (%, numer);
          (%o3)                   .6901942235215714

(%o1)                                true
(%i2) 

Quad_qawf Example

Related Examples

quad_qawf

? quad_qawf;

Calculate

quad_qawf

? quad_qawf;

Calculate