Formula:DLMF:25.2:E9: Difference between revisions
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<br /><div align="center"><math>{\displaystyle | <br /><div align="center"><math>{\displaystyle | ||
\RiemannZeta@{s} | |||
= \frac{1}{\EulerGamma@{s+1}} \int_0^\infty | |||
\frac{\expe^x x^s}{(\expe^x-1)^2} | |||
\diff{x}}</math></div> | |||
}</math></div> | |||
== Constraint(s) == | == Constraint(s) == |
Revision as of 21:53, 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.
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \RiemannZeta@{s} = \frac{1}{\EulerGamma@{s}} \int_0^\infty \frac{x^{s-1}}{\expe^x-1} \diff{x} }}
Symbols List
& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \zeta}}
: Riemann zeta function : http://dlmf.nist.gov/25.2#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}
: sum : http://drmf.wmflabs.org/wiki/Definition:sum
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}
: binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle B_{n}}}
: Bernoulli polynomial : http://dlmf.nist.gov/24.2#i
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}
: integral : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \widetilde{B}_{n}}}
: periodic Bernoulli functions : http://dlmf.nist.gov/24.2#iii
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{d}^nx}}
: differential : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Re {z}}}
: real part : http://dlmf.nist.gov/1.9#E2
Bibliography
Equation (9), Section 25.2 of DLMF.
URL links
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