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[Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result

 [Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result From: SourceForge.net - 2010-11-22 21:20:05 Bugs item #3105512, was opened at 2010-11-08 20:22 Message generated for change (Comment added) made by sf-robot You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&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: Works For Me Priority: 5 Private: No Submitted By: Andrzej Giniewicz (giniu) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result Initial Comment: integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1. ---------------------------------------------------------------------- >Comment By: SourceForge Robot (sf-robot) Date: 2010-11-22 21:20 Message: This Tracker item was closed automatically by the system. It was previously set to a Pending status, and the original submitter did not respond within 14 days (the time period specified by the administrator of this Tracker). ---------------------------------------------------------------------- Comment By: Andrzej Giniewicz (giniu) Date: 2010-11-08 21:40 Message: Indeed, I missed it I tested the diff on older version. Anyway, what is the reason for the difference in form of result in integrating (s^2 * exp(- (a+b) * s^2 )); and (s^2 * exp(- a * s^2 ));? ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2010-11-08 21:04 Message: I do not see a real problem, because we can verify the following: (%i1) (s^2 * exp(- (a+b) * s^2 )); (%o1) s^2*%e^((-b-a)*s^2) (%i2) integrate(%,s); (%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s)) (%i3) diff(%,s); (%o3) s^2*%e^-((b+a)*s^2) We get back the integrand. I have compared the result with a result from Wolfram alpha. It is possible to expand the integral in terms of the erf function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2). That is the result of this bug report too. But this is not an error. The result might be not the expected result, but it is not wrong. Setting the status to pending and the resolution to "works for me". Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&group_id=4933 

 [Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result From: SourceForge.net - 2010-11-08 20:22:28 Bugs item #3105512, was opened at 2010-11-08 21:22 Message generated for change (Tracker Item Submitted) made by giniu You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&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: Andrzej Giniewicz (giniu) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result Initial Comment: integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&group_id=4933 
 [Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result From: SourceForge.net - 2010-11-08 21:04:55 Bugs item #3105512, was opened at 2010-11-08 21:22 Message generated for change (Settings changed) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&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: Pending >Resolution: Works For Me Priority: 5 Private: No Submitted By: Andrzej Giniewicz (giniu) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result Initial Comment: integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1. ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2010-11-08 22:04 Message: I do not see a real problem, because we can verify the following: (%i1) (s^2 * exp(- (a+b) * s^2 )); (%o1) s^2*%e^((-b-a)*s^2) (%i2) integrate(%,s); (%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s)) (%i3) diff(%,s); (%o3) s^2*%e^-((b+a)*s^2) We get back the integrand. I have compared the result with a result from Wolfram alpha. It is possible to expand the integral in terms of the erf function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2). That is the result of this bug report too. But this is not an error. The result might be not the expected result, but it is not wrong. Setting the status to pending and the resolution to "works for me". Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&group_id=4933 
 [Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result From: SourceForge.net - 2010-11-08 21:40:03 Bugs item #3105512, was opened at 2010-11-08 21:22 Message generated for change (Comment added) made by giniu You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&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: Pending Resolution: Works For Me Priority: 5 Private: No Submitted By: Andrzej Giniewicz (giniu) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result Initial Comment: integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1. ---------------------------------------------------------------------- Comment By: Andrzej Giniewicz (giniu) Date: 2010-11-08 22:40 Message: Indeed, I missed it I tested the diff on older version. Anyway, what is the reason for the difference in form of result in integrating (s^2 * exp(- (a+b) * s^2 )); and (s^2 * exp(- a * s^2 ));? ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2010-11-08 22:04 Message: I do not see a real problem, because we can verify the following: (%i1) (s^2 * exp(- (a+b) * s^2 )); (%o1) s^2*%e^((-b-a)*s^2) (%i2) integrate(%,s); (%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s)) (%i3) diff(%,s); (%o3) s^2*%e^-((b+a)*s^2) We get back the integrand. I have compared the result with a result from Wolfram alpha. It is possible to expand the integral in terms of the erf function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2). That is the result of this bug report too. But this is not an error. The result might be not the expected result, but it is not wrong. Setting the status to pending and the resolution to "works for me". Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&group_id=4933 
 [Maxima-bugs] [ maxima-Bugs-3105512 ] integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result From: SourceForge.net - 2010-11-22 21:20:05 Bugs item #3105512, was opened at 2010-11-08 20:22 Message generated for change (Comment added) made by sf-robot You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&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: Works For Me Priority: 5 Private: No Submitted By: Andrzej Giniewicz (giniu) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(s^2 * exp(- (a+b) * s^2 ), s) returns bad result Initial Comment: integrate(s^2 * exp(- (a+b) * s^2 ), s); returns bad result, i.e. for example for s=1 it's off by \frac{\sqrt{pi}}{4(a+b)^{3/2}} (for s=1 it's easy to verify that it's bad answer). It would be correct if Erfc=-Erf, but it isn't of course - maybe some transformations in progress fail? What's funny, integrate(s^2 * exp(- a * s^2 ), s); works and gives correct result. I tested it with Maxima 5.22.1. ---------------------------------------------------------------------- >Comment By: SourceForge Robot (sf-robot) Date: 2010-11-22 21:20 Message: This Tracker item was closed automatically by the system. It was previously set to a Pending status, and the original submitter did not respond within 14 days (the time period specified by the administrator of this Tracker). ---------------------------------------------------------------------- Comment By: Andrzej Giniewicz (giniu) Date: 2010-11-08 21:40 Message: Indeed, I missed it I tested the diff on older version. Anyway, what is the reason for the difference in form of result in integrating (s^2 * exp(- (a+b) * s^2 )); and (s^2 * exp(- a * s^2 ));? ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2010-11-08 21:04 Message: I do not see a real problem, because we can verify the following: (%i1) (s^2 * exp(- (a+b) * s^2 )); (%o1) s^2*%e^((-b-a)*s^2) (%i2) integrate(%,s); (%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s)) (%i3) diff(%,s); (%o3) s^2*%e^-((b+a)*s^2) We get back the integrand. I have compared the result with a result from Wolfram alpha. It is possible to expand the integral in terms of the erf function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2). That is the result of this bug report too. But this is not an error. The result might be not the expected result, but it is not wrong. Setting the status to pending and the resolution to "works for me". Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3105512&group_id=4933