[Maxima-bugs] [ maxima-Bugs-2865951 ] specint(exp(-s*t)*bessel_y(0, a*t), t) not simplifed

 [Maxima-bugs] [ maxima-Bugs-2865951 ] specint(exp(-s*t)*bessel_y(0, a*t), t) not simplifed From: SourceForge.net - 2009-09-24 19:01:09 ```Bugs item #2865951, was opened at 2009-09-24 21:01 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&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: None 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)*bessel_y(0,a*t),t) not simplifed Initial Comment: We have a special algorithm in \$specint to express the Laplace transform of Bessel Y for an integer order in terms of the Associated Legendre Q function. Maxima knows this function and can simplify it. Unfortunately, the result of \$specint is not fully simplified: (%i2) assume(s>0)\$ (%i3) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o3) -2*legendre_q(0,s/sqrt(s^2+a^2))/(%pi*sqrt(s^2+a^2)) Because the Associated Legendre Q function is not implemented as a simplifying function we need an additional eval to get a simplified result: (%i4) ev(%); (%o4) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) It is easy to change this. We do not call legen in the routine leg2fsimp, which returns an unsimplifed noun form (legen m v z '\$q) but do a Maxima function call (the function is not in core and has to be autoloaded) (mfuncall '\$assoc_legendre_q m v z)) When we change the code, we get immediately the simplifed result: (%i6) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o6) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) This result is equivalent to -atanh(s/sqrt(s^2+a^2)/(%pi*sqrt(s^2+a^2)) The tabels I know give the result: -2*asinh(s/a)/(%pi*sqrt(s^2+a^2)) But this is equivalent to the atanh expression. We can show it with the help of the relation: atan(z)=1/2 * asinh(2*z/(z^2+1)) All expressions of the form t^n*bessel_y(v,t) with v an positive integer and n>=v will simplify accordingly. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-2865951 ] specint(exp(-s*t)*bessel_y(0, a*t), t) not simplifed From: SourceForge.net - 2009-09-24 19:01:09 ```Bugs item #2865951, was opened at 2009-09-24 21:01 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&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: None 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)*bessel_y(0,a*t),t) not simplifed Initial Comment: We have a special algorithm in \$specint to express the Laplace transform of Bessel Y for an integer order in terms of the Associated Legendre Q function. Maxima knows this function and can simplify it. Unfortunately, the result of \$specint is not fully simplified: (%i2) assume(s>0)\$ (%i3) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o3) -2*legendre_q(0,s/sqrt(s^2+a^2))/(%pi*sqrt(s^2+a^2)) Because the Associated Legendre Q function is not implemented as a simplifying function we need an additional eval to get a simplified result: (%i4) ev(%); (%o4) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) It is easy to change this. We do not call legen in the routine leg2fsimp, which returns an unsimplifed noun form (legen m v z '\$q) but do a Maxima function call (the function is not in core and has to be autoloaded) (mfuncall '\$assoc_legendre_q m v z)) When we change the code, we get immediately the simplifed result: (%i6) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o6) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) This result is equivalent to -atanh(s/sqrt(s^2+a^2)/(%pi*sqrt(s^2+a^2)) The tabels I know give the result: -2*asinh(s/a)/(%pi*sqrt(s^2+a^2)) But this is equivalent to the atanh expression. We can show it with the help of the relation: atan(z)=1/2 * asinh(2*z/(z^2+1)) All expressions of the form t^n*bessel_y(v,t) with v an positive integer and n>=v will simplify accordingly. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2865951 ] specint(exp(-s*t)*bessel_y(0, a*t), t) not simplifed From: SourceForge.net - 2009-09-24 19:02:08 ```Bugs item #2865951, was opened at 2009-09-24 21:01 Message generated for change (Settings changed) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&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)*bessel_y(0,a*t),t) not simplifed Initial Comment: We have a special algorithm in \$specint to express the Laplace transform of Bessel Y for an integer order in terms of the Associated Legendre Q function. Maxima knows this function and can simplify it. Unfortunately, the result of \$specint is not fully simplified: (%i2) assume(s>0)\$ (%i3) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o3) -2*legendre_q(0,s/sqrt(s^2+a^2))/(%pi*sqrt(s^2+a^2)) Because the Associated Legendre Q function is not implemented as a simplifying function we need an additional eval to get a simplified result: (%i4) ev(%); (%o4) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) It is easy to change this. We do not call legen in the routine leg2fsimp, which returns an unsimplifed noun form (legen m v z '\$q) but do a Maxima function call (the function is not in core and has to be autoloaded) (mfuncall '\$assoc_legendre_q m v z)) When we change the code, we get immediately the simplifed result: (%i6) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o6) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) This result is equivalent to -atanh(s/sqrt(s^2+a^2)/(%pi*sqrt(s^2+a^2)) The tabels I know give the result: -2*asinh(s/a)/(%pi*sqrt(s^2+a^2)) But this is equivalent to the atanh expression. We can show it with the help of the relation: atan(z)=1/2 * asinh(2*z/(z^2+1)) All expressions of the form t^n*bessel_y(v,t) with v an positive integer and n>=v will simplify accordingly. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2865951 ] specint(exp(-s*t)*bessel_y(0, a*t), t) not simplifed From: SourceForge.net - 2009-09-25 19:06:23 ```Bugs item #2865951, was opened at 2009-09-24 21:01 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&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)*bessel_y(0,a*t),t) not simplifed Initial Comment: We have a special algorithm in \$specint to express the Laplace transform of Bessel Y for an integer order in terms of the Associated Legendre Q function. Maxima knows this function and can simplify it. Unfortunately, the result of \$specint is not fully simplified: (%i2) assume(s>0)\$ (%i3) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o3) -2*legendre_q(0,s/sqrt(s^2+a^2))/(%pi*sqrt(s^2+a^2)) Because the Associated Legendre Q function is not implemented as a simplifying function we need an additional eval to get a simplified result: (%i4) ev(%); (%o4) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) It is easy to change this. We do not call legen in the routine leg2fsimp, which returns an unsimplifed noun form (legen m v z '\$q) but do a Maxima function call (the function is not in core and has to be autoloaded) (mfuncall '\$assoc_legendre_q m v z)) When we change the code, we get immediately the simplifed result: (%i6) specint(exp(-s*t)*bessel_y(0,a*t),t); (%o6) -log((sqrt(s^2+a^2)+s)/(sqrt(s^2+a^2)-s))/(%pi*sqrt(s^2+a^2)) This result is equivalent to -atanh(s/sqrt(s^2+a^2)/(%pi*sqrt(s^2+a^2)) The tabels I know give the result: -2*asinh(s/a)/(%pi*sqrt(s^2+a^2)) But this is equivalent to the atanh expression. We can show it with the help of the relation: atan(z)=1/2 * asinh(2*z/(z^2+1)) All expressions of the form t^n*bessel_y(v,t) with v an positive integer and n>=v will simplify accordingly. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2009-09-25 21:06 Message: Fixed in hypgeo.lisp revision 1.64. Closing this bug report. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2865951&group_id=4933 ```