Formula:DLMF:25.2:E9: Difference between revisions
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imported>SeedBot DRMF |
imported>Sahil No edit summary |
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== Constraint(s) == | == Constraint(s) == | ||
<div align="left"><math>{\displaystyle \realpart{s} > | <div align="left"><math>{\displaystyle \realpart{s} > 1}</math> | ||
<br /> | |||
== Proof == | == Proof == | ||
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<br /><br /> | <br /><br /> | ||
<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 /> | ||
\RiemannZeta@{s} | |||
= | |||
}</math><br /> | |||
by repeated integration by parts.</div> | by repeated integration by parts.</div> | ||
<br /> | <br /> |
Revision as of 21:51, 9 April 2017
Constraint(s)
Proof
We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.
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
We ask users to provide relevant URL links in this space.