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5.9.7  The cosine integral function:Ci

The Ci command takes as argument a complex number.
Ci returns the value of the cosine integral function Ci at the point, where

Ci(x) = 
x


+∞
 
cos(t)
t
 dt = ln(t) + γ +
x


t=0
 
cos(t) − 1
t
 dt

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

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