Formula:DLMF:25.5:E2: Difference between revisions
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<div align="center">{{#invoke:Math|render|P11}}</div> | |||
== Constraint(s) == | == Constraint(s) == | ||
<div align="left">{{#invoke:Math|render|P9}}</div | <div align="left">{{#invoke:Math|render|P9}}</div> | ||
== Proof == | == Proof == | ||
<div align="left">Integrate | |||
<math id="DLMF:25.5:E1" display=block>{\displaystyle | |||
<div align="left">Integrate | |||
<math id="DLMF:25.5:E1">{\displaystyle | |||
\RiemannZeta@{s} | \RiemannZeta@{s} | ||
= \frac{1}{\EulerGamma@{s}} | = \frac{1}{\EulerGamma@{s}} | ||
\int_0^\infty \frac{x^{s-1}}{\expe^x-1} \diff{x} | \int_0^\infty \frac{x^{s-1}}{\expe^x-1} \diff{x} | ||
}</math | }</math> | ||
by parts.</div> | by parts.</div> | ||
== Symbols List == | == Symbols List == | ||
Revision as of 08:43, 27 March 2017
Constraint(s)
Proof
Symbols List
: Riemann zeta function : http://dlmf.nist.gov/25.2#E1
: Euler's gamma function : http://dlmf.nist.gov/5.2#E1
: integral : http://dlmf.nist.gov/1.4#iv
: the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
: differential : http://dlmf.nist.gov/1.4#iv
: real part : http://dlmf.nist.gov/1.9#E2
Bibliography
Equation (2), Section 25.5 of DLMF.
URL links
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