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7.3.7  Cosine integral function

The cosine integral function is defined by

  Ci(x)=∫
x


+∞
 
cos(t)
t
 dt =ln(t)+γ+∫
x


0
 
cos(t)−1
t
 dt.

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

The Ci command computes the cosine integral function.

Examples

Ci(1.0)
     
0.337403922901           
Ci(-1.0)
     
0.337403922901+3.14159265359 i           
Ci(1.0)-Ci(-1.0)
     
−3.14159265359 i           
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