Cosine integral

The cosine integral 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

References

• Generalized Sine and Cosine Integrals

$\ast$-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