WOLFRAM|DEMONSTRATIONS PROJECT

Trigonometric Integral Functions

​
3D plot
contour plot
real part
imaginary part
absolute value
function
Chi(z)
Ci(z)
Shi(z)
Si(z)
Ei(z)
The trigonometric integrals are special functions defined as
Chi(z)=γ+
z
∫
0
cosh(t)-1
t
t+log(z)
,
Ci(z)=γ+
z
∫
0
cos(t)-1
t
t+log(z)
,
Shi(z)=
z
∫
0
sinh(t)
t
t
,
Si(z)=
z
∫
0
sin(t)
t
t
,
Ei(z)=-
∞
∫
-z
-t

t
t
. As functions of a complex variable, they can be visualized by plotting their real part, imaginary part, or absolute value.