Re: Question on Nest[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg15055] Re: [mg15006] Question on Nest[]*From*: Jurgen Tischer <jtischer at col2.telecom.com.co>*Date*: Wed, 9 Dec 1998 04:12:35 -0500*Organization*: Universidad del Valle*References*: <199812050630.BAA04480@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Wagner, I think a lot depends on what you need (and what you mean by efficient). Since you obviously want numerical results, the first choice for me would be to use NSum. It's not very fast but has checks built in which make you feel better than trying to invent your own formula. If this turns out to lame for your needs, try FunctionInterpolation (you better define f by something like f[m_?NumericQ]:=...). I checked it for the interval [0,2] and it was good for some 5 digits. If this is too low in precision, use the options on NSum and on FunctionInterpolation. Jurgen Wagner Truppel wrote: > > Howdy, > > I'm (still) trying to evaluate the sum > > f[m_] := E^(-m) Sum[ m^i Sqrt[i] / i!, { i, 1.0, Infinity } ] > > in an efficient way. I tried compiling this expression, but Mathematica > refused to compile i!. I then replaced i! by Gamma[i+1.0], but then I > get compilation errors due to the arbitrary precision nature of the > computation. Finally, I decided to try someting based on the identity: > > Sum[ m^i Sqrt[i] / i!, { i, 1.0, n } ] = m/1 ( Sqrt[1] + m/2 ( Sqrt[2] + > m/3 ( Sqrt[3] + ... + Sqrt[n] ) ) ) ) > > So I tried > > i = 0.0; > Expand[ Nest[ ( i++; m/i ( Sqrt[i] + # ) )&, 0, n ] ] > > but it doesn't produce the correct polynomial in m. What am I missing?? > > Thanks in advance for any help. > > Wagner

**References**:**Question on Nest[]***From:*Wagner Truppel <wtruppel@uci.edu>