## maxima-bugs

 [Maxima-bugs] [ maxima-Bugs-2867434 ] specint(exp(-s*t)*t^2*%h[1, 1](t), t) does not work From: SourceForge.net - 2009-09-26 13:36:00 ```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 ```
 [Maxima-bugs] [ maxima-Bugs-2867434 ] specint(exp(-s*t)*t^2*%h[1, 1](t), t) does not work From: SourceForge.net - 2009-09-26 18:52:20 ```Bugs item #2867434, was opened at 2009-09-26 15:35 Message generated for change (Settings changed) 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: Closed >Resolution: Fixed 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 ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2009-09-26 20:52 Message: Fixed in hypgeo.lisp revision 1.66. Closing this bug report. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2867434&group_id=4933 ```