[Maxima-bugs] [ maxima-Bugs-2847436 ] integrate(sqrt(t)*log(t)^(1/2), t, 0, 1) wrong sign From: SourceForge.net - 2009-08-30 21:27:34 ```Bugs item #2847436, was opened at 2009-08-30 21:27 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(t)*log(t)^(1/2),t,0,1) wrong sign Initial Comment: The following two integrals have the wrong sign: integrate(sqrt(t)*log(t)^(1/2),t,0,1) and integrate(sqrt(t)*log(t)^(-1/2),t,0,1) It is interesting that Maxima is able to solve the more general type: (%i164) declare(s,noninteger); (%o164) done (%i165) expr:integrate(sqrt(t)*log(t)^s,t,0,1); (%o165) 3^(-s-1)*(-1)^s*2^(s+1)*gamma_incomplete(s+1,0) For s=1/2 and s=-1/2 we get the answers: (%i167) expr,s=1/2; (%o167) sqrt(2)*sqrt(%pi)*%i/(2*sqrt(3)) (%i168) expr,s=-1/2; (%o168) -sqrt(2)*sqrt(%pi)*%i/sqrt(3) Both solutions can be checked to be correct. Now we do it directly: (%i4) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o4) -%i*('limit(sqrt(2)*sqrt(%pi)*erf(sqrt(3)*sqrt(-log(t))/sqrt(2))/3^(3/2) -2*t^(3/2)*sqrt(-log(t))/3,t,0,plus)) We need an extra evaluation, but this is another problem: (%i5) %,nouns; (%o5) -sqrt(2)*sqrt(%pi)*%i/3^(3/2) Now the integral for s=-1/2: (%i6) integrate(sqrt(t)*log(t)^(-1/2),t,0,1); (%o6) sqrt(2)*sqrt(%pi)*%i/sqrt(3) These solutions differ by the sign with the answers from above. I have checked it for a lot of other values for the parameter s. In all other cases the result of the integral and the more general solution are equal. Remark: The integral is divergent for s a negative integer. For these cases the gamma_incomplete function is not defined. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2847436 ] integrate(sqrt(t)*log(t)^(1/2), t, 0, 1) wrong sign From: SourceForge.net - 2009-08-30 21:27:34 ```Bugs item #2847436, was opened at 2009-08-30 21:27 Message generated for change (Tracker Item Submitted) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(t)*log(t)^(1/2),t,0,1) wrong sign Initial Comment: The following two integrals have the wrong sign: integrate(sqrt(t)*log(t)^(1/2),t,0,1) and integrate(sqrt(t)*log(t)^(-1/2),t,0,1) It is interesting that Maxima is able to solve the more general type: (%i164) declare(s,noninteger); (%o164) done (%i165) expr:integrate(sqrt(t)*log(t)^s,t,0,1); (%o165) 3^(-s-1)*(-1)^s*2^(s+1)*gamma_incomplete(s+1,0) For s=1/2 and s=-1/2 we get the answers: (%i167) expr,s=1/2; (%o167) sqrt(2)*sqrt(%pi)*%i/(2*sqrt(3)) (%i168) expr,s=-1/2; (%o168) -sqrt(2)*sqrt(%pi)*%i/sqrt(3) Both solutions can be checked to be correct. Now we do it directly: (%i4) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o4) -%i*('limit(sqrt(2)*sqrt(%pi)*erf(sqrt(3)*sqrt(-log(t))/sqrt(2))/3^(3/2) -2*t^(3/2)*sqrt(-log(t))/3,t,0,plus)) We need an extra evaluation, but this is another problem: (%i5) %,nouns; (%o5) -sqrt(2)*sqrt(%pi)*%i/3^(3/2) Now the integral for s=-1/2: (%i6) integrate(sqrt(t)*log(t)^(-1/2),t,0,1); (%o6) sqrt(2)*sqrt(%pi)*%i/sqrt(3) These solutions differ by the sign with the answers from above. I have checked it for a lot of other values for the parameter s. In all other cases the result of the integral and the more general solution are equal. Remark: The integral is divergent for s a negative integer. For these cases the gamma_incomplete function is not defined. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2847436 ] integrate(sqrt(t)*log(t)^(1/2), t, 0, 1) wrong sign From: SourceForge.net - 2010-02-04 14:41:29 ```Bugs item #2847436, was opened at 2009-08-30 17:27 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(t)*log(t)^(1/2),t,0,1) wrong sign Initial Comment: The following two integrals have the wrong sign: integrate(sqrt(t)*log(t)^(1/2),t,0,1) and integrate(sqrt(t)*log(t)^(-1/2),t,0,1) It is interesting that Maxima is able to solve the more general type: (%i164) declare(s,noninteger); (%o164) done (%i165) expr:integrate(sqrt(t)*log(t)^s,t,0,1); (%o165) 3^(-s-1)*(-1)^s*2^(s+1)*gamma_incomplete(s+1,0) For s=1/2 and s=-1/2 we get the answers: (%i167) expr,s=1/2; (%o167) sqrt(2)*sqrt(%pi)*%i/(2*sqrt(3)) (%i168) expr,s=-1/2; (%o168) -sqrt(2)*sqrt(%pi)*%i/sqrt(3) Both solutions can be checked to be correct. Now we do it directly: (%i4) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o4) -%i*('limit(sqrt(2)*sqrt(%pi)*erf(sqrt(3)*sqrt(-log(t))/sqrt(2))/3^(3/2) -2*t^(3/2)*sqrt(-log(t))/3,t,0,plus)) We need an extra evaluation, but this is another problem: (%i5) %,nouns; (%o5) -sqrt(2)*sqrt(%pi)*%i/3^(3/2) Now the integral for s=-1/2: (%i6) integrate(sqrt(t)*log(t)^(-1/2),t,0,1); (%o6) sqrt(2)*sqrt(%pi)*%i/sqrt(3) These solutions differ by the sign with the answers from above. I have checked it for a lot of other values for the parameter s. In all other cases the result of the integral and the more general solution are equal. Remark: The integral is divergent for s a negative integer. For these cases the gamma_incomplete function is not defined. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2010-02-04 09:41 Message: The definite integral is computed by doing the indefinite integral via rischint. The limits are then taken. For some reason limit cannot evaluate the limit, which explains the noun form in the result. In addition, the limit at 0 is done by breaking the result into real and imaginary parts and taking the limit of each and putting them back together. The limit of the real part is 0, but the limit of the imaginary part has the incorrect sign. Perhaps the imaginary part is computed incorrectly? ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2847436 ] integrate(sqrt(t)*log(t)^(1/2), t, 0, 1) wrong sign From: SourceForge.net - 2010-03-16 08:50:38 ```Bugs item #2847436, was opened at 2009-08-30 17:27 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&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: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(t)*log(t)^(1/2),t,0,1) wrong sign Initial Comment: The following two integrals have the wrong sign: integrate(sqrt(t)*log(t)^(1/2),t,0,1) and integrate(sqrt(t)*log(t)^(-1/2),t,0,1) It is interesting that Maxima is able to solve the more general type: (%i164) declare(s,noninteger); (%o164) done (%i165) expr:integrate(sqrt(t)*log(t)^s,t,0,1); (%o165) 3^(-s-1)*(-1)^s*2^(s+1)*gamma_incomplete(s+1,0) For s=1/2 and s=-1/2 we get the answers: (%i167) expr,s=1/2; (%o167) sqrt(2)*sqrt(%pi)*%i/(2*sqrt(3)) (%i168) expr,s=-1/2; (%o168) -sqrt(2)*sqrt(%pi)*%i/sqrt(3) Both solutions can be checked to be correct. Now we do it directly: (%i4) integrate(sqrt(t)*log(t)^(1/2),t,0,1); (%o4) -%i*('limit(sqrt(2)*sqrt(%pi)*erf(sqrt(3)*sqrt(-log(t))/sqrt(2))/3^(3/2) -2*t^(3/2)*sqrt(-log(t))/3,t,0,plus)) We need an extra evaluation, but this is another problem: (%i5) %,nouns; (%o5) -sqrt(2)*sqrt(%pi)*%i/3^(3/2) Now the integral for s=-1/2: (%i6) integrate(sqrt(t)*log(t)^(-1/2),t,0,1); (%o6) sqrt(2)*sqrt(%pi)*%i/sqrt(3) These solutions differ by the sign with the answers from above. I have checked it for a lot of other values for the parameter s. In all other cases the result of the integral and the more general solution are equal. Remark: The integral is divergent for s a negative integer. For these cases the gamma_incomplete function is not defined. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dan Gildea (dgildea) Date: 2010-03-16 04:50 Message: Fixed in sin.lisp 1.58. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2010-02-04 09:41 Message: The definite integral is computed by doing the indefinite integral via rischint. The limits are then taken. For some reason limit cannot evaluate the limit, which explains the noun form in the result. In addition, the limit at 0 is done by breaking the result into real and imaginary parts and taking the limit of each and putting them back together. The limit of the real part is 0, but the limit of the imaginary part has the incorrect sign. Perhaps the imaginary part is computed incorrectly? ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847436&group_id=4933 ```