Cosine integral

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

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  Graph of $\mathrm{Ci}$.

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  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): $\S 5 (5.10)$

$\ast$-integral functions

Cosine integral

Cosh integral

Exp integral $E_n$

Exp integral $\mathrm{Ei}$

Fresnel $C$

Fresnel $S$

Gudermannian

Inverse $\mathrm{gd}$

Sine integral

Log integral

Sinh integral