Now that Acer's Method (looks like amazing magic from where I'm at) has solved Maple's issues calculating the integral:
int(BesselJ(0, 50001*x)*x*exp((355/2)*x^2*I), x = 35/100 .. 1)
can anyone use Acer's method to produce the graph that is "...a Fresnel diffraction pattern (in Mathematica [Maple]) which gave the answer to the problem…"?
The following is a stripped down version of Dr. Dermot Hogan's "Real Life Test" from his comparison of Mathematica and Maple:
"The question was whether a particular telescope’s obstruction was 35% or 42%.
"With a telescope, the diffraction pattern produced by the wave nature of light when the telescope eyepiece is at focus is simple ‘Fraunhofer’ diffraction. A long way off, and you see the aperture of the telescope with the shadow of the secondary clearly obstructing it – you might call this the ‘geometric’ case. And in between is ‘Fresnel’ diffraction.
"The trouble with Fresnel diffraction is that it is tricky to compute. Indeed, before the advent of fast computers and packages like Maple and Mathematica, it just wasn’t computed. For a circular aperture, the computation involves a complex oscillatory integral with Bessel functions which can only be evaluated by numerical methods.
"with the eyepiece at maximum distance from the focus, the measured size of the central obstruction’s shadow was indeed 42% for a 35% physical obstruction.
... This is a Fresnel diffraction pattern (in Mathematica) which gave the answer to the problem…"
As you can see, the plot abscissa runs from 0 to 0.002. 35% of 0.002 is 0.00070 and 42% of 0.002 is 0.00082. I'm having trouble trying to decide if that spacial pulse is 0.00082 wide (42%) and Dr. Hogan was right or is the pulse width 0.00070 (35%) or is there to much computational noise to decide or what?