Function intdeo
I = integral of f(x) over (a,infinity), f(x) has oscillatory factor :
void intdeo(Real, Func)
(
Func f,
Real a,
Real omega,
Real eps,
Real* i,
Real* err
);
f(x) = g(x) * sin(omega * x + theta) as x -> infinity
Parameters
Name | Description |
---|---|
f | integrand f(x) |
a | lower limit of integration |
omega | frequency of oscillation |
eps | relative error requested |
i | approximation to the integral |
err | estimate of the absolute error |
Remarks
function f(x) needs to be analytic over (a,infinity). relative error eps is relative error requested excluding cancellation of significant digits. i.e. eps means : (absolute error) / (integral_a^R |f(x)| dx). eps does not mean : (absolute error) / I. error message err >= 0 : normal termination. err < 0 : abnormal termination (m >= mmax). i.e. convergent error is detected : 1. f(x) or (d/dx)^n f(x) has discontinuous points or sharp peaks over (a,infinity). you must divide the interval (a,infinity) at this points. 2. relative error of f(x) is greater than eps.