Re: Closed Form solution too much to hope for?

*To*: mathgroup at smc.vnet.net*Subject*: [mg66845] Re: Closed Form solution too much to hope for?*From*: "Valeri Astanoff" <astanoff at yahoo.fr>*Date*: Thu, 1 Jun 2006 06:55:00 -0400 (EDT)*References*: <e5augm$no4$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Assuming mean(x) is about .75, here is an empirical formula that might be useful to you: In[1]:=x[c_,d_,n_]:=Sqrt[c](d-1)(2d-1)+c^(1/n)d(2d-1)- (2(d-1)d(-2n+Sqrt[2]Sqrt[36c+n(9+2n+9Log[4/3])-9(1+Log[2])]))/3 In[2]:=x[c,0,n] Out[2]=Sqrt[c] In[3]:=x[c,1,n] Out[3]=c^(1/n) In[4]:=x[.5,.6,9] Out[4]=0.88615 In[5]:=FindRoot[d x^n+(1-d)x^2==c /. c -> .5 /. d -> .6 /. n -> 9,{x,.5}] Out[5]={x -> 0.880133} hth V.Astanoff