Difference between revisions of "Relationship between exponential integral Ei, cosine integral, and sine integral"
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<strong>[[Relationship between exponential integral Ei, cosine integral, and sine integral|Theorem]]:</strong> The following formula holds: | <strong>[[Relationship between exponential integral Ei, cosine integral, and sine integral|Theorem]]:</strong> The following formula holds: | ||
| − | $$Ei(ix)=\mathrm{Ci}(x)+i\mathrm{Si}(x),$$ | + | $$\mathrm{Ei}(ix)=\mathrm{Ci}(x)+i\mathrm{Si}(x),$$ |
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]]. | ||
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Revision as of 01:21, 2 December 2015
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.
Proof: █
