Re: sequence of functions
- To: mathgroup at smc.vnet.net
- Subject: [mg120199] Re: sequence of functions
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Tue, 12 Jul 2011 07:01:02 -0400 (EDT)
- References: <201107080855.EAA28789@smc.vnet.net> <iv9eqf$dfb$1@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
> Bobby, f[n_][x_] := f[n][x] = ... results in caching for not only > each n and each x. "...for not only each n, but also for each x...", you mean. Good point! Here's another solution, without that defect: ClearAll[f, x] f[0] = # (1 - #) &; f[n_Integer?Positive] := With[{s = Simplify[f[n - 1][2 #] + f[n - 1][2 # - 1]]}, f[n] = s &] or ClearAll[f, x] f[0] = # (1 - #) &; f[n_Integer?Positive] := With[{s = FullSimplify[f[n - 1][2 #] + f[n - 1][2 # - 1]]}, f[n] = s &] Bobby On Mon, 11 Jul 2011 05:56:58 -0500, rych <rychphd at gmail.com> wrote: > Yes, indeed, wrapping it with Evaluate did it. Thanks, Heike. > > Bobby, f[n_][x_] := f[n][x] = ... results in caching for not only > each n and each x. > > Dana, how did you apply FindSequenceFunction to get the direct > formula?! > > Thanks > Igor > > > > On Jul 9, 11:42 pm, Heike Gramberg <heike.gramb... at gmail.com> wrote: >> What about >> >> f[0] = Function[x, x (1 - x)] >> f[n_] := f[n] = >> Function[x, Evaluate[Simplify[f[n - 1][2 x] + f[n - 1][2 x - 1]]]]; >> >> Then >> >> f[2][x]; >> ?f >> >> returns: >> >> Global`f >> f[0]=Function[x,x (1-x)] >> f[1]=Function[x$,-2 (1-2 x$)^2] >> f[2]=Function[x$,-20+64 x$-64 x$^2] >> f[n_]:=f[n]=Function[x,Evaluate[Simplify[f[n-1][2 x]+f[n-1][2 x-1]]]] >> >> Heike > > -- DrMajorBob at yahoo.com
- References:
- sequence of functions
- From: rych <rychphd@gmail.com>
- sequence of functions