[Maxima-bugs] [ maxima-Bugs-2867434 ] specint(exp(-s*t)*t^2*%h[1, 1](t), t) does not work

[SourceForge.net <no...@so...>]

Bugs item #2867434, was opened at 2009-09-26 15:35
Message generated for change (Tracker Item Submitted) made by crategus
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2867434&group_id=4933

Please note that this message will contain a full copy of the comment thread,
including the initial issue submission, for this request,
not just the latest update.
Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: specint(exp(-s*t)*t^2*%h[1,1](t),t) does not work

Initial Comment:
We know

   hankel_1(v,z) = bessel_j(v,z) + %i * bessel_y(v,z) and
   hankel_2(v,z) = bessel_j(v,z) - %i * bessel_y(v,z).

If we try to get the Laplace transform of %h[v,sort](z), that is the Hankel function known to specint, we get:

(%i2) specint(exp(-s*t)*t^2*%h[1,1](t),t);
Division by 0
 -- an error.  To debug this try debugmode(true);

(%i3) specint(exp(-s*t)*t^2*%h[1,2](t),t);
Division by 0
 -- an error.  To debug this try debugmode(true);

But both Laplace transforms Maxima can calculate:

(%i7) factor(ratsimp(specint(exp(-s*t)*t^2*(bessel_j(1,t)+%i*bessel_y(1,t)),t)));
(%o7) (3*s*sqrt(s^2+1)*log((sqrt(s^2+1)+s)/(sqrt(s^2+1)-s))
       +3*%pi*s*sqrt(s^2+1)+2*s^4-2*s^2-4)
       /(%pi*(s^2+1)^3)

(%i8) factor(ratsimp(specint(exp(-s*t)*t^2*(bessel_j(1,t)-%i*bessel_y(1,t)),t)));
(%o8) (3*s*sqrt(s^2+1)*log((sqrt(s^2+1)+s)/(sqrt(s^2+1)-s))
       +3*%pi*s*sqrt(s^2+1)+2*s^4-2*s^2-4)
       /(%pi*(s^2+1)^3)

The error for the hankel functions %h[v,sort](t) occurs, because the transformation to Bessel J and Bessel Y functions is implemented wrongly in the routine htjory.

Dieter Kaiser

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2867434&group_id=4933