Formula:DLMF:25.2:E9: Difference between revisions

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== Constraint(s) ==
== Constraint(s) ==
 
{{#invoke:Wd|properties|P9|format=%p<br/>}}
<div align="left"><math>{\displaystyle \realpart{s} > -2n} </math>
<br /> <math>{\displaystyle n,N = 1,2,3,\dots} </math>
<br />


== Proof ==
== Proof ==

Revision as of 16:04, 2 January 2020


Constraint(s)



Proof

Follows from


by repeated integration by parts.

Symbols List

& : logical and
 : Riemann zeta function : http://dlmf.nist.gov/25.2#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 (9), Section 25.2 of DLMF.

URL links

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