sequence of functions
- To: mathgroup at smc.vnet.net
- Subject: [mg120110] sequence of functions
- From: rych <rychphd at gmail.com>
- Date: Fri, 8 Jul 2011 04:55:33 -0400 (EDT)
I would like to build a function sequence inductively, for example f[n][x]=f[n-1][2x]+f[n-1][2x-1], f[0][x] = x(1-x) This is what I tried in Mathematica, ClearAll["Global`*"] f[n_] = Function[x, Simplify[f[n - 1][2 x] + f[n - 1][2 x - 1]]]; f[0] = Function[x, x (1 - x)]; f[2][x] Out: -20 + 64 x - 64 x^2 ?f Out: Global`f f[0]=Function[x,x (1-x)] f[n_]=Function[x,Simplify[f[n-1][2 x]+f[n-1][2 x-1]]] My questions: it doesn't seem to cache the previous f[n-1] etc? If I do it this way instead, f[n_] := f[n] = Function[... Then it does cache the f[n-1] etc. but still in the unevaluated form, Global`f f[0]=Function[x,x (1-x)] f[1]=Function[x$,Simplify[f[1-1][2 x$]+f[1-1][2 x$-1]]] f[2]=Function[x$,Simplify[f[2-1][2 x$]+f[2-1][2 x$-1]]] f[n_]:=f[n]=Function[x,Simplify[f[n-1][2 x]+f[n-1][2 x-1]]] How do I force the reduction so that I see f[1] = -2 (1 - 2 x)^2, etc. in the definitions? Thanks, Igor
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