Relation With The Exponential Integral of Imaginary Argument
The function
is called the exponential integral. It is closely related to Si and Ci:
As each involved function is analytic except the cut at negative values of the argument, the area of validity of the relation should be extended to . (Out of this range, additional terms which are integer factors of appear in the expression).
Cases of imaginary argument of the generalized integro-exponential function are
which is the real part of
Similarly
Read more about this topic: Trigonometric Integral
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