Difference between revisions of "Exponential integral Ei series"
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<strong>[[Exponential integral Ei series|Theorem]]:</strong> The following formula holds: | <strong>[[Exponential integral Ei series|Theorem]]:</strong> The following formula holds: | ||
$$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!}; x>0,$$ | $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!}; x>0,$$ | ||
| − | where $\mathrm{Ei}$ denotes the [[exponential integral]], $\log$ denotes the [[logarithm]], and $\gamma$ denotes the [[Euler-Mascheroni constant]]. | + | where $\mathrm{Ei}$ denotes the [[exponential integral Ei]], $\log$ denotes the [[logarithm]], and $\gamma$ denotes the [[Euler-Mascheroni constant]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 22:08, 16 August 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 Ei, $\log$ denotes the logarithm, and $\gamma$ denotes the Euler-Mascheroni constant.
Proof: █
