6.8.7  The cosine integral function: Ci

The cosine integral function is defined by

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