Difference between revisions of "Exponential integral Ei series"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds for $x>0$: | |
| − | $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!} | + | $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!},$$ |
where $\mathrm{Ei}$ denotes the [[exponential integral Ei]], $\log$ denotes the [[logarithm]], and $\gamma$ denotes the [[Euler-Mascheroni constant]]. | where $\mathrm{Ei}$ denotes the [[exponential integral Ei]], $\log$ denotes the [[logarithm]], and $\gamma$ denotes the [[Euler-Mascheroni constant]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 07:00, 4 June 2016
Theorem
The following formula holds for $x>0$: $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!},$$ where $\mathrm{Ei}$ denotes the exponential integral Ei, $\log$ denotes the logarithm, and $\gamma$ denotes the Euler-Mascheroni constant.
