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the integration contour is a loop around the negative real axis; it starts at , encircles the origin once in the positive direction without enclosing any of the points

, and returns to


We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Assume , collapse the integration path onto the

real axis, apply


followed by analytic continuation.

Symbols List

& : logical and
 : Hurwitz zeta function :
 : Euler's gamma function :
 : ratio of a circle's circumference to its diameter :
 : integral :
 : the base of the natural logarithm :
 : differential :
 : real part :


Equation (30), Section 25.11 of DLMF.

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