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2nd RE: Functional decomposition (solving f[f[x]] = g[x] for given g)

• To: mathgroup at smc.vnet.net
• Subject: [mg71819] 2nd RE: [mg71764] Functional decomposition (solving f[f[x]] = g[x] for given g)
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Thu, 30 Nov 2006 06:05:14 -0500 (EST)
• Reply-to: <ingolf.dahl at telia.com>

Addendum to answer:

 

Hi again,

Now the "Inverse Symbolic Calculator" at
http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html is up and working,

Extract from search for f(0) = 0.6420945043908285:

 

"6420944524139337 = (0261) 1+2*x+4*x^2+3*x^3-4*x^4-x^5
6420944718605426 = (0191) Prod(1-(3*n^3-8*n^2+3*n+10)/2^n,n=1..inf)
Your value of 6420945043908285 would be here.
6420945157426995 = (0001) Lehmer*(BesJ(1,1)+Cahen)

6420945315416897 = (0001) (GAM(5/6)-GaussK)/GAM(17/24)"

 

Best regards

 

Ingolf Dahl