I think it needs to be fixed. Here is an example of the error.
The a value in the log gamma function LGAMMA3(z,a,m) is too
small for large negative real arguments. The a value can be
increased by increasing the precision.
The a value does the same as n!=(n+1)!/(n+1).
The a value makes negative arguments more positive.
InputMode:=Word
PrecisionDigits:=12
NotationDigits:=12
APPROX((-11.75)!,6)
;Simp(#4)
-2.04424*10^(-7)+2.04424*10^(-7)*#i
APPROX((-11.75)!,7)
;Simp(#6)
-2.04423*10^(-7)
APPROX((-11.75)!,12)
;Simp(#8)
-2.04422991204*10^(-7)
LGAMMA3(z,a,m):=(2*a-1)*LN((z+a)/a)/2+z*LN(z+a)-LN(z)+SUM((a^(-2*j_+1)-(z+a)
^~
(-2*j_+1))*ZETA(1-2*j_)/(2*j_-1),j_,1,m)+SUM(LN(k/(k+z)),k,1,a-1)-z
EXP(LGAMMA3(-10.75,8,4))
;Approx(#11)
-2.04423006219*10^(-7)+2.0442300622*10^(-7)*#i
EXP(LGAMMA3(-10.75,13,4))
;Approx(#13)
-2.04422907924*10^(-7)
Jim FitzSimons
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-----Original Message-----
From: DERIVE computer algebra system [mailto:[log in to unmask]] On
Behalf Of Jaime Marcos
Sent: Friday, January 14, 2005 11:17 AM
To: [log in to unmask]
Subject: Unexpected Complex Values in Factorial
Dear Derivians,
With the DfW 5.06 if you try to get, for instance, (-40.625)! in exact
mode, you get a rational expression times (3/8)!, that simplifies in turn
(working with 25 significant digits) to
1.6 669898 143291 70810 E-47. Fine.
But if you try to get (directly) the approximate value of (-40.625)!, you
get an ugly complex,
2.845729616210276126327153·10^-47 - 1.178739801881079045325915·10^-47 ·î
Does it happen the same thing in DfW 6.1?
Best wishes for the 2005,
Jaime Marcos
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