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I am looking for a tight upper bound of exponential function (or sum of exponential functions):

$e^x<f(x)$ when $x<0$ or

$\sum_{i=1}^n e^{x_i} < g(x_1,...,x_n)$ when $x_i<0$

Thanks a lot!

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3  
If $x < 0$ then $e^x < 1$. Is this what you need? –  Pragabhava Oct 10 '12 at 18:07
1  
What do you mean with $x$ is discrete? –  Hagen von Eitzen Oct 10 '12 at 18:42
    
Thanks Pragabhava, but I am looking for a tight upper bound of exponential function. –  Mehran Oct 10 '12 at 19:32
    
Thanks Pragabhava, but I am looking for a tight upper bound for exponential function. I know a close upper bound ($1/(1-x)$) , but I am looking for polynomial form! –  Mehran Oct 10 '12 at 19:39
    
Sorry, "x is discrete" was a mistake. –  Mehran Oct 10 '12 at 19:48
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