Formula:DLMF:25.11:E7

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Constraint(s)

&
&
&


Proof

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Take in


and integrate by parts.


Symbols List

& : logical and
 : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
 : sum : http://drmf.wmflabs.org/wiki/Definition:sum
 : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
 : Bernoulli polynomial : http://dlmf.nist.gov/24.2#i
 : integral : http://dlmf.nist.gov/1.4#iv
 : periodic Bernoulli functions : http://dlmf.nist.gov/24.2#iii
 : differential : http://dlmf.nist.gov/1.4#iv
 : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (7), Section 25.11 of DLMF.

URL links

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