Shi

The hyperbolic sine integral is defined by the formula $$\mathrm{Shi}(z)=\displaystyle\int_0^z \dfrac{\mathrm{sinh}(t)}{t} dt.$$

• 

  Plot of $\mathrm{Shi}$ on $[-10,10]$.

• 

  Domain coloring of analytic continuation of $\mathrm{Shi}$.

<center>$\ast$-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

</center>