intdeo

I = integral of f(x) over (a,infinity), f(x) has oscillatory factor :

f(x) = g(x) * sin(omega * x + theta) as x -> infinity

void

intdeo

(

Real

Func

)

(

Func f

Real a

Real eps

Real* i

Real* err

)

Parameters

f Func: integrand f(x)
a Real: lower limit of integration
omega Real: frequency of oscillation
eps Real: relative error requested
i Real*: approximation to the integral
err Real*: estimate of the absolute error
Remarks: <pre> 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. </pre>