## #1775 specint(exp(-s*t)*t^2*%h[1,1](t),t) does not work

closed
nobody
5
2009-09-26
2009-09-26
No

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

## Discussion

• Dieter Kaiser - 2009-09-26

Fixed in hypgeo.lisp revision 1.66. Closing this bug report.

Dieter Kaiser

• Dieter Kaiser - 2009-09-26
• status: open --> closed

## Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:

No, thanks