Formula:DLMF:25.11:E30
Constraint(s)
&
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
Proof
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Symbols List
& : logical and
: Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
: Euler's gamma function : http://dlmf.nist.gov/5.2#E1
: ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
: integral : http://dlmf.nist.gov/1.4#iv
: the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
: differential : http://dlmf.nist.gov/1.4#iv
: real part : http://dlmf.nist.gov/1.9#E2
Bibliography
Equation (30), Section 25.11 of DLMF.
URL links
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