Formula:DLMF:25.11:E30

From DRMF
Jump to: navigation, search


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

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

and

followed by analytic continuation.


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

We ask users to provide relevant URL links in this space.