Difference between revisions of "Relationship between exponential integral Ei, cosine integral, and sine integral"

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==Theorem==
<strong>[[Relationship between exponential integral Ei, cosine integral, and sine integral|Theorem]]:</strong> The following formula holds:
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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]].
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<strong>Proof:</strong>  █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[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.

Proof

References