rtoy
commented
4 months ago Imported from SourceForge on 2024-07-02 19:13:55 Created by crategus on 2009-09-26 18:52:17 Original: https://sourceforge.net/p/maxima/bugs/1775/#8384
Fixed in hypgeo.lisp revision 1.66. Closing this bug report.
Dieter Kaiser
Imported from SourceForge on 2024-07-02 19:13:54 Created by crategus on 2009-09-26 13:35:59 Original: https://sourceforge.net/p/maxima/bugs/1775
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