Difference between revisions of "Exponential integral Ei series"
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==References== | ==References== | ||
| − | * {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|prev=Ei(-x)=-Integral from x to infinity of e^(-t)/t dt|next= | + | * {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|prev=Ei(-x)=-Integral from x to infinity of e^(-t)/t dt|next=Logarithmic integral}} (<i>note: expresses the logarithm term as $\frac{1}{4}\log(x^4)$</i>) |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 03:31, 17 March 2018
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.
Proof
References
- James Whitbread Lee Glaisher: On certain definite integrals involving the exponential-integral (1881)... (previous)... (next) (note: expresses the logarithm term as $\frac{1}{4}\log(x^4)$)
