Difference between revisions of "Cosine integral"
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| − | The cosine integral is defined by | + | __NOTOC__ |
| − | $$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} | + | The cosine integral, $\mathrm{Ci}$, is defined by |
| + | $$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} \mathrm{d}t, \quad |\mathrm{arg} z|<\pi.$$ | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Ciplot.png|Graph of $\mathrm{Ci}$. |
| − | File: | + | File:Complexciplot.png|[[Domain coloring]] of $\mathrm{Ci}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | =Relationship to other functions= | ||
| + | [[Derivative of cosine integral]]<br /> | ||
| + | [[Antiderivative of cosine integral]]<br /> | ||
| + | [[Relationship between exponential integral Ei, cosine integral, and sine integral]]<br /> | ||
=Videos= | =Videos= | ||
| − | [https://www.youtube.com/watch?v=BAme-njI8sE Laplace transform of cosine integral] | + | [https://www.youtube.com/watch?v=BAme-njI8sE Laplace transform of cosine integral (2 January 2015)] |
=References= | =References= | ||
| − | * | + | * {{BookReference|Special Functions of Mathematical Physics and Chemistry|1956|Ian N. Sneddon|prev=findme|next=Sine integral}}: $\S 5 (5.10)$ |
| − | + | {{:*-integral functions footer}} | |
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 15:43, 11 July 2017
The cosine integral, $\mathrm{Ci}$, is defined by $$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} \mathrm{d}t, \quad |\mathrm{arg} z|<\pi.$$
Graph of $\mathrm{Ci}$.
Domain coloring of $\mathrm{Ci}$.
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
- 1956: Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry ... (previous) ... (next): $\S 5 (5.10)$
