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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$$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} \mathrm{d}t, \quad |\mathrm{arg} z|<\pi.$$
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Ci.png|Graph of $\mathrm{arccos}$ on $(0,20)$.
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File:Ciplot.png|Graph of $\mathrm{Ci}$.
File:Domain coloring cosine integral.png|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{Ci}$.
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File:Complexciplot.png|[[Domain coloring]] of $\mathrm{Ci}$.
 
</gallery>
 
</gallery>
 
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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 />
  
 
=Videos=
 
=Videos=
[https://www.youtube.com/watch?v=BAme-njI8sE Laplace transform of cosine integral]
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[https://www.youtube.com/watch?v=BAme-njI8sE Laplace transform of cosine integral (2 January 2015)]
  
 
=References=
 
=References=
*[http://dlmf.nist.gov/8.21 Generalized Sine and Cosine Integrals]
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* {{BookReference|Special Functions of Mathematical Physics and Chemistry|1956|Ian N. Sneddon|prev=findme|next=Sine integral}}: $\S 5 (5.10)$
  
<center>{{:*-integral functions footer}}</center>
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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