## [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 - 2004-12-30 07:05:09 ```Bugs item #1093138, was opened at 2004-12-30 00:05 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 Category: Lisp Core Group: None Status: Open Resolution: None Priority: 3 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). ---------------------------------------------------------------------- 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 - 2004-12-30 07:05:09 ```Bugs item #1093138, was opened at 2004-12-30 00:05 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 Category: Lisp Core Group: None Status: Open Resolution: None Priority: 3 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). ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1093138&group_id=4933 ```