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MathGroup Archive 2004

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LogIntegral^(-1)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48620] LogIntegral^(-1)
  • From: "Roger L. Bagula" <rlbtftn at netscape.net>
  • Date: Tue, 8 Jun 2004 00:48:11 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I have an information theory problem:
Suppose that the noise has a constant expectation value with time
so that when you take the differential you get
DN/dt=0
Mathematica for the Shannon capascity as rate of transmission is:
s1[t_]=D[s[t],t]
n[t_]=s[t]/(Exp[s1[t]/w]-1)
n1[t_]=D[n[t],t]
DSolve[FullSimplify[n1[t]]==0,s[t],t]

I get an answer involving:
LogIntegral^(-1)
specifically:

s[t_]=C[2]*(-1+LogIntegral^(-1)[w*(t-C[1])/C[2]])

I'm pretty sure that C[2] represents the average noise.
The problem is I can't get Mathematica to plot this function.
I replaced c2 and c1 with real constants and used a constant w
while trying to plot Re[s[t]]:
I get errors like:
Plot::"plnr":
     "\!\(Re[\(s[t]\)]\) is not a machine-size real number at \!\(t\) = \
\!\(-0.999999916666666699`\)."
Plot::"plnr":
     \:f3b5\!\(Re[s[t]]\) is not a machine-size real number at t = \
-0.918866016854168421`.
Plot::"plnr":
     "\!\(Re[\(s[t]\)]\) is not a machine-size real number at \!\(t\) = \
\!\(-0.830382400281252586`\)."
General::"stop":
     "Further output of \!\(Plot :: \"plnr\"\) will be suppressed during 
this \
calculation."


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