Difference between revisions of "Exponential integral Ei series"

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Revision as of 01:43, 21 March 2015

Theorem: The following formula holds: $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!}; x>0,$$ where $\mathrm{Ei}$ denotes the exponential integral, $\log$ denotes the logarithm, and $\gamma$ denotes the Euler-Mascheroni constant.

Proof: