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
PrecisionDigits:=25
NotationDigits:=25
(-40.625)!
;Approx(#17)
2.845729616210276126327150*10^(-47)-1.178739801881079045325914*10^(-47)*#i
;Simp(#17)
10633823966279326983230456482242756608*(3/8)!/567043081750808808419344961695
6~
07275219754948897795872564094615106803215935263671875
;Approx(#19)
1.666989814329197081001235*10^(-47)
EXP(LGAMMA3(-39.625,70,9))-1.666989814329197081001235*10^(-47)
;Approx(#21)
1.640682843699673893797797*10^(-71)
The a value needs to be 70 to get 25 digits of precision using the log gamma
function LGAMMA3(z,a,m). DERIVE must be using an a value that is too small.
Jim FitzSimons
-----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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