Difference between revisions of "Relationship between logarithmic integral and exponential integral"

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==Theorem==
<strong>[[Relationship between logarithmic integral and exponential integral|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$\mathrm{li}(x)=\mathrm{Ei}( \log(x)),$$
 
$$\mathrm{li}(x)=\mathrm{Ei}( \log(x)),$$
 
where $\mathrm{li}$ denotes the [[logarithmic integral]], $\mathrm{Ei}$ denotes the [[exponential integral Ei]], and $\log$ denotes the [[logarithm]].
 
where $\mathrm{li}$ denotes the [[logarithmic integral]], $\mathrm{Ei}$ denotes the [[exponential integral Ei]], and $\log$ denotes the [[logarithm]].
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<strong>Proof:</strong>
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==Proof==
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==References==
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* {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|prev=Logarithmic integral|next=findme}} (<i>note: expresses this relationship as $\mathrm{Ei}(x)=\mathrm{li}(e^x)$</i>)
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 03:34, 17 March 2018

Theorem

The following formula holds: $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)),$$ where $\mathrm{li}$ denotes the logarithmic integral, $\mathrm{Ei}$ denotes the exponential integral Ei, and $\log$ denotes the logarithm.

Proof

References