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

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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)),$$ where $\mathrm{li}$ denot...")
 
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<strong>Theorem:</strong> The following formula holds:
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<strong>[[Relationship between logarithmic integral and exponential integral|Theorem]]:</strong> 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]] and $\mathrm{Ei}$ denotes the [[exponential integral]].
 
where $\mathrm{li}$ denotes the [[logarithmic integral]] and $\mathrm{Ei}$ denotes the [[exponential integral]].

Revision as of 06:45, 5 April 2015

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

Proof: