- 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*(-1+LogIntegral^(-1)[w*(t-C)/C]) I'm pretty sure that C 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."