Question on Nest[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg15006] Question on Nest[]*From*: Wagner Truppel <wtruppel at uci.edu>*Date*: Sat, 5 Dec 1998 01:30:11 -0500*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Question on Nest[]***From:*Jurgen Tischer <jtischer@col2.telecom.com.co>