# The cosine integral function: Ci

### 5.8.7 The cosine integral function: Ci

The cosine integral function is defined by

Ci(x)

=

∫

x
+∞

cos(t)
t

dt

=ln(t) + γ +

∫

x
t=0

cos(t) − 1
t

dt

and Ci(0) = −∞, Ci(−∞) = iπ and Ci(+∞) = 0.

The Ci command computes the cosine integral function.

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

#### Examples.

- Input:
  Ci(1.0)
  Output:

  0.337403922901

- Input:
  Ci(-1.0)
  Output:

  0.337403922901+3.14159265359 i

- Input:
  Ci(1.0) - Ci(-1.0)
  Output:

  −3.14159265359 i