Re: need a hand ordering functions
- To: mathgroup at smc.vnet.net
- Subject: [mg16676] Re: [mg16566] need a hand ordering functions
- From: BobHanlon at aol.com
- Date: Fri, 19 Mar 1999 12:54:24 -0500
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 3/18/99 9:27:53 AM, money00 at angelfire.com writes:
>The problem is, i have have six functions
>
>1) n log n
>2) n^8 (n to the power of eight)
>3) n^1+a (n to the power of one plus a)
>4) (1+a)^n (one plus a to the power of n)
>5) n^2 / logn (n squared over log n)
>6) (n^2 - n+1)^4 (n squared minus n plus one to the power of four)
>
>now using the relations "proper subset" and "equals" i have to put the
>above into a sequence where "a" is the arbitrary real constant, 0<a<1.
>
Needs["Graphics`Graphics`"];
Needs["Graphics`Legend`"];
I have assumed that when you wrote n^1+a that you meant n^(1+a).
funcs = { n*Log[n], n^8,n^(1+a), (1+a)^n,
n^2 / Log[n], (n^2 - n + 1)^4};
You can investigate the plots of the functions
ShowLegend[LogPlot[Evaluate[funcs /. a -> .5], {n, 1.25, 3},
PlotStyle -> Table[Hue[h], {h, 0, 1, 1/6}],
DisplayFunction -> Identity],
{Hue[5#/6]&, 6, "1","6", LegendPosition -> {1.1, -.4}}];
Alternatively, you can investigate the series expansions in n
Collect[Expand[Normal[Series[#, {n, 2., 8}]]]& /@ (funcs /. a->.5), n]//
ColumnForm
Bob Hanlon