confused!
- To: mathgroup at smc.vnet.net
- Subject: [mg78900] confused!
- From: dimitris <dimmechan at yahoo.com>
- Date: Thu, 12 Jul 2007 05:20:30 -0400 (EDT)
Hello.
(version 5.2)
Say
In[201]:=
g[z_] := RootSum[1 + #1^2 + #1^3 & , (Log[-I + z]*Log[1 - (-I + z)/(-I
+ #1)] + PolyLog[2, (-I + z)/(-I + #1)])/
(2*#1 + 3*#1^2) & ] + RootSum[1 + #1^2 + #1^3 & , (Log[I +
z]*Log[1 - (I + z)/(I + #1)] + PolyLog[2, (I + z)/(I + #1)])/(2*#1 +
3*#1^2) & ]
Then
In[208]:=
Plot[g[z], {z, 0, 10}]
In[209]:=
disc =
z /. ToRadicals[ToRules[Reduce[Im[1 - (I + z)/((-(1/3) + I) +
(1/6)*(1 + I*Sqrt[3])*((1/2)*(29 - 3*Sqrt[93]))^(1/3) +
(1 - I*Sqrt[3])/(3*2^(2/3)*(29 - 3*Sqrt[93])^(1/3)))] == 0
&& Im[z] == 0, z]]]
Out[209]=
(4 - 2*(29/2 + (3*Sqrt[93])/2)^(1/3) - 2*(2/(29 + 3*Sqrt[93]))^(1/3))/
(-12 + 2*Sqrt[3]*(29/2 + (3*Sqrt[93])/2)^(1/3) -
2*Sqrt[3]*(2/(29 + 3*Sqrt[93]))^(1/3))
Should the following limits be different?
In[235]:=
(Limit[g[z],z\[Rule]disc,Direction\[Rule]#]&)/@{-1,1}//N[#,120]&
Out[235]=
{-1.93280687058518544591333323341099018662625381606406087872262908094261623587\
579018111126672955973274498162595572599953216-0.\
352799929636499065742936342802253119059635973423462632768775400341025881430703\
16101859237983014877085731418268885248465 \
\[ImaginaryI],-1.\
932806870585185445913333233410990186626253816064060878722629080942616235875790\
18111126672955973274498162595572599953216-0.\
352799929636499065742936342802253119059635973423462632768775400341025881430703\
16101859237983014877085731418268885248465 \[ImaginaryI]}
Dimitris
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