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Question on Nest[]


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


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