Formula:DLMF:25.5:E4

From DRMF
Jump to navigation Jump to search


Failed to parse (unknown function "\RiemannZeta"): {\displaystyle {\displaystyle \RiemannZeta@{s} = \frac{1}{(1 - 2^{1-s}) \EulerGamma@{s+1}} \int_0^\infty \frac{\expe^x x^s}{(\expe^x+1)^2} \diff{x} }}

Constraint(s)

Failed to parse (unknown function "\realpart"): {\displaystyle {\displaystyle \realpart{s} > 0}} &


Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Integrate

Failed to parse (unknown function "\RiemannZeta"): {\displaystyle {\displaystyle \RiemannZeta@{s} = \frac{1}{(1 - 2^{1-s}) \EulerGamma@{s}} \int_0^\infty \frac{x^{s-1}}{\expe^x+1} \diff{x} }}

by parts.


Symbols List

& : logical and
 : 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 (4), Section 25.5 of DLMF.

URL links

We ask users to provide relevant URL links in this space.