## [Maxima-bugs] [ maxima-Bugs-2847387 ] hgfred([3/2, -b], [5/2], -1) bogus

 [Maxima-bugs] [ maxima-Bugs-2847387 ] hgfred([3/2, -b], [5/2], -1) bogus From: SourceForge.net - 2009-08-30 18:54:01 ```Bugs item #2847387, was opened at 2009-08-30 20:53 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&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 Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: hgfred([3/2,-b],[5/2],-1) bogus Initial Comment: The general result for the definite integral integrate(sqrt(t)*(t+1)^b,t,0,1) is 2/3*hypergeometric([3/2,-b],[5/2],-1). The new hypergeometric code gives correct answers for b a positive integer: (%i128) 2/3*hypergeometric([3/2,-1],[5/2],-1); (%o128) 16/15 (%i129) 2/3*hypergeometric([3/2,-2],[5/2],-1); (%o129) 184/105 (%i130) 2/3*hypergeometric([3/2,-3],[5/2],-1); (%o130) 928/315 For negative integers I have tried hgfred. This is an example for b=-3: (%i112) 2/3*hgfred([3/2,3],[5/2],-1); (%o112) (12*((-1/(2*(1-(-"*"()))^3*(-1))+5/(8*(1-(-"*"()))^2*(-1)^2) -15/(16*(1-(-"*"()))*(-1)^3) +15*atanh(sqrt(-1))/(16*(-1)^(7/2)) -3/(1-(-"*"()))^4) *sqrt(1-(-"*"())) -2*(-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) /sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*(2*sqrt(1-(-"*"())))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(2*(1-(-"*"()))^(5/2)) -15*(1-atanh(sqrt(-1))*sqrt(-1))/(16*(1-(-"*"()))^(7/2))) *(2*sqrt(1-(-"*"())))*(-1)^2 -36*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *sqrt(1-(-"*"()))*(-1)^2 +9*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"())))))*(-1)^2 /sqrt(1-(-"*"())) -48*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *(2*sqrt(1-(-"*"())))*1 +72*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *sqrt(1-(-"*"()))*1 +24*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *(2*sqrt(1-(-"*"())))) /3 The answer is not simplified and contains bad subexpressions. But if we do an extra expand we get the correct solution: (%i113) expand(%); (%o113) %pi/16 We have the same problem with other negative integers for b too. For a positive integer we get an answer in terms of the jacobi_p function which does not simplify to a rational number. There is a problem with b=2: (%i124) 2/3*hgfred([3/2,-2],[5/2],-1); (%o124) 16*jacobi_p(2,3/2,2*false-5/2,3)/105 The answer contains the boolean value false. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-2847387 ] hgfred([3/2, -b], [5/2], -1) bogus From: SourceForge.net - 2009-08-30 18:54:01 ```Bugs item #2847387, was opened at 2009-08-30 20:53 Message generated for change (Tracker Item Submitted) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&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 Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: hgfred([3/2,-b],[5/2],-1) bogus Initial Comment: The general result for the definite integral integrate(sqrt(t)*(t+1)^b,t,0,1) is 2/3*hypergeometric([3/2,-b],[5/2],-1). The new hypergeometric code gives correct answers for b a positive integer: (%i128) 2/3*hypergeometric([3/2,-1],[5/2],-1); (%o128) 16/15 (%i129) 2/3*hypergeometric([3/2,-2],[5/2],-1); (%o129) 184/105 (%i130) 2/3*hypergeometric([3/2,-3],[5/2],-1); (%o130) 928/315 For negative integers I have tried hgfred. This is an example for b=-3: (%i112) 2/3*hgfred([3/2,3],[5/2],-1); (%o112) (12*((-1/(2*(1-(-"*"()))^3*(-1))+5/(8*(1-(-"*"()))^2*(-1)^2) -15/(16*(1-(-"*"()))*(-1)^3) +15*atanh(sqrt(-1))/(16*(-1)^(7/2)) -3/(1-(-"*"()))^4) *sqrt(1-(-"*"())) -2*(-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) /sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*(2*sqrt(1-(-"*"())))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(2*(1-(-"*"()))^(5/2)) -15*(1-atanh(sqrt(-1))*sqrt(-1))/(16*(1-(-"*"()))^(7/2))) *(2*sqrt(1-(-"*"())))*(-1)^2 -36*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *sqrt(1-(-"*"()))*(-1)^2 +9*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"())))))*(-1)^2 /sqrt(1-(-"*"())) -48*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *(2*sqrt(1-(-"*"())))*1 +72*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *sqrt(1-(-"*"()))*1 +24*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *(2*sqrt(1-(-"*"())))) /3 The answer is not simplified and contains bad subexpressions. But if we do an extra expand we get the correct solution: (%i113) expand(%); (%o113) %pi/16 We have the same problem with other negative integers for b too. For a positive integer we get an answer in terms of the jacobi_p function which does not simplify to a rational number. There is a problem with b=2: (%i124) 2/3*hgfred([3/2,-2],[5/2],-1); (%o124) 16*jacobi_p(2,3/2,2*false-5/2,3)/105 The answer contains the boolean value false. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2847387 ] hgfred([3/2, -b], [5/2], -1) bogus From: SourceForge.net - 2009-09-03 16:45:49 ```Bugs item #2847387, was opened at 2009-08-30 14:53 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&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 Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: hgfred([3/2,-b],[5/2],-1) bogus Initial Comment: The general result for the definite integral integrate(sqrt(t)*(t+1)^b,t,0,1) is 2/3*hypergeometric([3/2,-b],[5/2],-1). The new hypergeometric code gives correct answers for b a positive integer: (%i128) 2/3*hypergeometric([3/2,-1],[5/2],-1); (%o128) 16/15 (%i129) 2/3*hypergeometric([3/2,-2],[5/2],-1); (%o129) 184/105 (%i130) 2/3*hypergeometric([3/2,-3],[5/2],-1); (%o130) 928/315 For negative integers I have tried hgfred. This is an example for b=-3: (%i112) 2/3*hgfred([3/2,3],[5/2],-1); (%o112) (12*((-1/(2*(1-(-"*"()))^3*(-1))+5/(8*(1-(-"*"()))^2*(-1)^2) -15/(16*(1-(-"*"()))*(-1)^3) +15*atanh(sqrt(-1))/(16*(-1)^(7/2)) -3/(1-(-"*"()))^4) *sqrt(1-(-"*"())) -2*(-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) /sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*(2*sqrt(1-(-"*"())))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(2*(1-(-"*"()))^(5/2)) -15*(1-atanh(sqrt(-1))*sqrt(-1))/(16*(1-(-"*"()))^(7/2))) *(2*sqrt(1-(-"*"())))*(-1)^2 -36*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *sqrt(1-(-"*"()))*(-1)^2 +9*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"())))))*(-1)^2 /sqrt(1-(-"*"())) -48*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *(2*sqrt(1-(-"*"())))*1 +72*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *sqrt(1-(-"*"()))*1 +24*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *(2*sqrt(1-(-"*"())))) /3 The answer is not simplified and contains bad subexpressions. But if we do an extra expand we get the correct solution: (%i113) expand(%); (%o113) %pi/16 We have the same problem with other negative integers for b too. For a positive integer we get an answer in terms of the jacobi_p function which does not simplify to a rational number. There is a problem with b=2: (%i124) 2/3*hgfred([3/2,-2],[5/2],-1); (%o124) 16*jacobi_p(2,3/2,2*false-5/2,3)/105 The answer contains the boolean value false. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2009-09-03 12:45 Message: I think the fundamental issue is that hgfred is meant for symbolic work with symbolic argument. Now, for the first problem, hgfred([3/2,2],[5/2],-1) does something bad probably from the call to subst at the end of hyp-atanh. Perhaps it should use \$subst. The second problem with jacobi_p is another example of where maxima is assuming the argument is symbolic, not numeric. Since people use hgfred all the time with numeric argument, perhaps hgfred should either warn/error about that, or it should replace the argument with a gensym, do the simplification, and then subst/limit the result with the numeric argument. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-2847387 ] hgfred([3/2, -b], [5/2], -1) bogus From: SourceForge.net - 2009-10-10 21:17:42 ```Bugs item #2847387, was opened at 2009-08-30 20:53 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&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 Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Dieter Kaiser (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: hgfred([3/2,-b],[5/2],-1) bogus Initial Comment: The general result for the definite integral integrate(sqrt(t)*(t+1)^b,t,0,1) is 2/3*hypergeometric([3/2,-b],[5/2],-1). The new hypergeometric code gives correct answers for b a positive integer: (%i128) 2/3*hypergeometric([3/2,-1],[5/2],-1); (%o128) 16/15 (%i129) 2/3*hypergeometric([3/2,-2],[5/2],-1); (%o129) 184/105 (%i130) 2/3*hypergeometric([3/2,-3],[5/2],-1); (%o130) 928/315 For negative integers I have tried hgfred. This is an example for b=-3: (%i112) 2/3*hgfred([3/2,3],[5/2],-1); (%o112) (12*((-1/(2*(1-(-"*"()))^3*(-1))+5/(8*(1-(-"*"()))^2*(-1)^2) -15/(16*(1-(-"*"()))*(-1)^3) +15*atanh(sqrt(-1))/(16*(-1)^(7/2)) -3/(1-(-"*"()))^4) *sqrt(1-(-"*"())) -2*(-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) /sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*(2*sqrt(1-(-"*"())))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(2*(1-(-"*"()))^(5/2)) -15*(1-atanh(sqrt(-1))*sqrt(-1))/(16*(1-(-"*"()))^(7/2))) *(2*sqrt(1-(-"*"())))*(-1)^2 -36*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *sqrt(1-(-"*"()))*(-1)^2 +9*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"())))))*(-1)^2 /sqrt(1-(-"*"())) -48*((-1/(4*(1-(-"*"()))^2*(-1))+3/(8*(1-(-"*"()))*(-1)^2) -3*atanh(sqrt(-1))/(8*(-1)^(5/2)) -1/(1-(-"*"()))^3) *sqrt(1-(-"*"())) -3*(-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) /(2*sqrt(1-(-"*"()))) -3*(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /(4*(2*sqrt(1-(-"*"())))) -3*(1-atanh(sqrt(-1))*sqrt(-1))/(8*(1-(-"*"()))^(5/2))) *(2*sqrt(1-(-"*"())))*1 +72*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *sqrt(1-(-"*"()))*1 +24*((-1/(4*(1-(-"*"()))*(-1))+atanh(sqrt(-1))/(4*(2*sqrt(-1))) -1/(2*(1-(-"*"()))^2)) *sqrt(1-(-"*"())) -(-atanh(sqrt(-1))/(2*sqrt(-1))-1/(2*(1-(-"*"())))) /sqrt(1-(-"*"())) -(1-atanh(sqrt(-1))*sqrt(-1))/(4*(2*sqrt(1-(-"*"()))))) *(2*sqrt(1-(-"*"())))) /3 The answer is not simplified and contains bad subexpressions. But if we do an extra expand we get the correct solution: (%i113) expand(%); (%o113) %pi/16 We have the same problem with other negative integers for b too. For a positive integer we get an answer in terms of the jacobi_p function which does not simplify to a rational number. There is a problem with b=2: (%i124) 2/3*hgfred([3/2,-2],[5/2],-1); (%o124) 16*jacobi_p(2,3/2,2*false-5/2,3)/105 The answer contains the boolean value false. Dieter Kaiser ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2009-10-10 23:17 Message: Both problems of this bug report are fixed in hyp.lisp revision 1.108. Closing this bug report as fixed. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2009-09-03 18:45 Message: I think the fundamental issue is that hgfred is meant for symbolic work with symbolic argument. Now, for the first problem, hgfred([3/2,2],[5/2],-1) does something bad probably from the call to subst at the end of hyp-atanh. Perhaps it should use \$subst. The second problem with jacobi_p is another example of where maxima is assuming the argument is symbolic, not numeric. Since people use hgfred all the time with numeric argument, perhaps hgfred should either warn/error about that, or it should replace the argument with a gensym, do the simplification, and then subst/limit the result with the numeric argument. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2847387&group_id=4933 ```