[Maxima-bugs] [ maxima-Bugs-1093138 ] double factorial defn incorrect for noninteger operand

 [Maxima-bugs] [ maxima-Bugs-1093138 ] double factorial defn incorrect for noninteger operand From: SourceForge.net - 2008-09-27 12:30:37 ```Bugs item #1093138, was opened at 2004-12-30 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&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: None Priority: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x-2)*(x-4)*...*y, where y is the least term (x-2*k) s.t. x-2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows -- doublefact (z) := block ([a: 1+2*z-cos(%pi*z), b: cos(%pi*z)-1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2). ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2008-09-27 14:30 Message: Closing this bug report. The function \$genfact(x,y,z) no longer gives wrong results. A function factorial_double has been implemented. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2008-09-22 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-1093138 ] double factorial defn incorrect for noninteger operand From: SourceForge.net - 2008-09-21 22:17:58 ```Bugs item #1093138, was opened at 2004-12-30 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&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: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x-2)*(x-4)*...*y, where y is the least term (x-2*k) s.t. x-2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows -- doublefact (z) := block ([a: 1+2*z-cos(%pi*z), b: cos(%pi*z)-1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2). ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2008-09-22 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1093138 ] double factorial defn incorrect for noninteger operand From: SourceForge.net - 2008-09-27 12:30:37 ```Bugs item #1093138, was opened at 2004-12-30 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&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: None Priority: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x-2)*(x-4)*...*y, where y is the least term (x-2*k) s.t. x-2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows -- doublefact (z) := block ([a: 1+2*z-cos(%pi*z), b: cos(%pi*z)-1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2). ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2008-09-27 14:30 Message: Closing this bug report. The function \$genfact(x,y,z) no longer gives wrong results. A function factorial_double has been implemented. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2008-09-22 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1093138 ] double factorial defn incorrect for noninteger operand From: SourceForge.net - 2008-09-27 19:16:12 ```Bugs item #1093138, was opened at 2004-12-30 08:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&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: 3 Private: No Submitted By: Robert Dodier (robert_dodier) Assigned to: Nobody/Anonymous (nobody) Summary: double factorial defn incorrect for noninteger operand Initial Comment: The double factorial x!! yields an incorrect result for x other than an integer. It appears that x!! is computed as the product x*(x-2)*(x-4)*...*y, where y is the least term (x-2*k) s.t. x-2*k > 1. This agrees with published defns (Arfken, Mathworld) for positive integers but not otherwise. Mathworld (http://mathworld.wolfram.com/DoubleFactorial.html) states a formula for z!!, z complex, translated into Maxima as follows -- doublefact (z) := block ([a: 1+2*z-cos(%pi*z), b: cos(%pi*z)-1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2)); It seems that Maxima could evaluate this function for noninteger arguments. Note that Maxima translates input x!! into an noun form genfact (x, x/2, 2). ---------------------------------------------------------------------- >Comment By: Dieter Kaiser (crategus) Date: 2008-09-27 21:16 Message: Change resolution to "fixed". ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2008-09-27 14:30 Message: Closing this bug report. The function \$genfact(x,y,z) no longer gives wrong results. A function factorial_double has been implemented. Dieter Kaiser ---------------------------------------------------------------------- Comment By: Dieter Kaiser (crategus) Date: 2008-09-22 00:17 Message: In a first step (asum.lisp, Rev. 1.30) the numerical evaluation of the function genfact(x,y,z) is specialized to integer arguments within the following range x, y, z, integer and z <= x and y <= x/z. For non valid integers a Maxima error is thrown. For all other numbers Maxima returns a noun form. With this changes Maxima no longer calculate wrong results. To get more general results for real and complex values for the Double factorial function a new function factorial_double has been suggested on the mailing list. Because Maxima no longer gets incorrect results this bug report could be closed. Dieter Kaiser ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 ```