Difference between revisions of "Relationship between exponential integral Ei, cosine integral, and sine integral"
From specialfunctionswiki
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− | + | ==Theorem== | |
− | + | The following formula holds: | |
$$\mathrm{Ei}(ix)=\mathrm{Ci}(x)+i\mathrm{Si}(x),$$ | $$\mathrm{Ei}(ix)=\mathrm{Ci}(x)+i\mathrm{Si}(x),$$ | ||
where $\mathrm{Ei}$ denotes the [[exponential integral Ei]], $\mathrm{Ci}$ denotes the [[cosine integral]], and $\mathrm{Si}$ denotes the [[sine integral]]. | where $\mathrm{Ei}$ denotes the [[exponential integral Ei]], $\mathrm{Ci}$ denotes the [[cosine integral]], and $\mathrm{Si}$ denotes the [[sine integral]]. | ||
− | + | ||
− | + | ==Proof== | |
− | + | ||
− | + | ==References== | |
+ | |||
+ | [[Category:Theorem]] | ||
+ | [[Category:Unproven]] |
Latest revision as of 08:03, 8 June 2016
Theorem
The following formula holds: $$\mathrm{Ei}(ix)=\mathrm{Ci}(x)+i\mathrm{Si}(x),$$ where $\mathrm{Ei}$ denotes the exponential integral Ei, $\mathrm{Ci}$ denotes the cosine integral, and $\mathrm{Si}$ denotes the sine integral.