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

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Bugs item #1093138, was opened at 2004-12-30 00:05
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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).


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