### 7.3.7 Cosine integral function

The cosine integral function is defined by

Ci(x)= | ∫ |
x
+∞
cos(t)
t
| d t =ln(t)+γ+ | ∫ |
x
0
cos(t)−1
t
| d t.

It can be shown that Ci(0)=−∞, Ci(−∞)=iπ and Ci(+∞)=0.

The Ci command computes the cosine integral function.

- Ci takes z, a complex number.
- Ci(z) returns the value of the cosine integral function Ci(z).

#### Examples

Ci(1.0)

0.337403922901 |  |  |  |  |  |  |  |  |  |

Ci(-1.0)

0.337403922901+3.14159265359 i |  |  |  |  |  |  |  |  |  |

Ci(1.0)-Ci(-1.0)

−3.14159265359 i |  |  |  |  |  |  |  |  |  |