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

$e^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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    If $x < 0$ then $e^x < 1$. Is this what you need?2012-10-10
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    What do you mean with $x$ is discrete?2012-10-10
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    Thanks Pragabhava, but I am looking for a tight upper bound of exponential function.2012-10-10
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    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!2012-10-10
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    Sorry, "x is discrete" was a mistake.2012-10-10

3 Answers 3