Formula:DLMF:25.2:E9: Difference between revisions
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<br /><div align="center" | <br /><div align="center">{{#invoke:Wd|property|P1|}}</div> | ||
== Constraint(s) == | == Constraint(s) == | ||
{{#invoke:Wd|properties|P9|format=%p<br/>}} | |||
<br /> | |||
== Proof == | == Proof == | ||
<div align="left">Follows from <br /> | <div align="left">Follows from <br /> | ||
<math id="DLMF:25.2:E8">{\displaystyle \ | <math id="DLMF:25.2:E8">{\displaystyle \Riemannzeta@{s} = \frac{1}{\EulerGamma@{s}} \int_0^\infty \frac{x^{s-1}}{\expe^x-1} \diff{x} }</math><br /> | ||
by repeated integration by parts.</div> | by repeated integration by parts.</div> | ||
== Symbols List == | == Symbols List == | ||
<ul>{{#invoke:Wd|properties|linked|raw|qualifier|P4|P1|format=<li>%q: %p</li>}}</ul> | |||
& : logical and<br /> | & : logical and<br /> |
Latest revision as of 18:09, 2 January 2020
Constraint(s)
Proof
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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