====== 지수합 함수 (Exponential Sum Function) ======
===== 정의 =====
 $$ \begin{displaymath}\begin{split} e_{n}(x) &= \sum_{k=0}^{n} \frac{x^{k}}{k!} \\ &= \frac{e^{x} \Gamma(n+1,x)}{\Gamma(n+1)} \end{split}\end{displaymath} $$

<plot>
 set size 1.0
 set xrange [0:10]
 set yrange [0:10]
 set zeroaxis
 set title "Exponential Sum Function"

 f(x,n) = ((exp(x))*(gamma(n+1)-igamma(n+1,x)))/(gamma(n+1))

 plot f(x,0.0) title "n=0", \
  f(x,1.0) title "n=1", \
  f(x,2.0) title "n=2", \
  f(x,3.0) title "n=3"
</plot>

 단, $\Gamma(x)$는 [[감마함수]], $\Gamma(a,x)$는 [[불완전 감마함수]]이다.

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  * [[함수]]