Difference between revisions of "Cosine integral"

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The cosine integral is defined by
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$$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} dt ; |\mathrm{arg} z|<\pi.$$
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The cosine integral, $\mathrm{Ci}$, is defined by
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$$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} \mathrm{d}t, \quad |\mathrm{arg} z|<\pi.$$
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<div align="center">
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<gallery>
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File:Ciplot.png|Graph of $\mathrm{Ci}$.
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File:Complexciplot.png|[[Domain coloring]] of $\mathrm{Ci}$.
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</gallery>
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</div>
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=Relationship to other functions=
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[[Derivative of cosine integral]]<br />
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[[Antiderivative of cosine integral]]<br />
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[[Relationship between exponential integral Ei, cosine integral, and sine integral]]<br />
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=Videos=
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[https://www.youtube.com/watch?v=BAme-njI8sE Laplace transform of cosine integral (2 January 2015)]
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=References=
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* {{BookReference|Special Functions of Mathematical Physics and Chemistry|1956|Ian N. Sneddon|prev=findme|next=Sine integral}}: $\S 5 (5.10)$
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{{:*-integral functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 15:43, 11 July 2017

The cosine integral, $\mathrm{Ci}$, is defined by $$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} \mathrm{d}t, \quad |\mathrm{arg} z|<\pi.$$

Relationship to other functions

Derivative of cosine integral
Antiderivative of cosine integral
Relationship between exponential integral Ei, cosine integral, and sine integral

Videos

Laplace transform of cosine integral (2 January 2015)

References

$\ast$-integral functions