Exponential Sum Function

Author

Eric W. Weisstein
August 8, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/ExponentialSumFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ExponentialSumFunction.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

ExpSum[n_,x_]:=(((E^x) Gamma[1+n,x])/(Gamma[1+n]))

Plot[Evaluate[Table[ExpSum[n,x],{n,0,5}]],{x,-5,1},
AxesLabel->TraditionalForm/@{x,(Subscript[e, n])[x]},
PlotStyle->{Black,Red,Yellow,Green,Blue,Violet}]

Sums

FullSimplify[Sum[x^k/k!,{k,0,n}]]

Sum[x^k/k!,{k,0,n-1}]

FullSimplify[%]

FullSimplify[(n-1)!(1-Exp[-x]Sum[x^k/k!,{s,0,k-1}])]