Formula:DLMF:25.11:E10

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Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta@{s}{a} = \sum_{n=0}^\infty \frac{\EulerGamma@{n+s}}{n! \EulerGamma@{s}} \RiemannZeta@{n+s} (1-a)^n }}

Constraint(s)

&


Proof

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Use Taylor's theorem and

Failed to parse (unknown function "\pderiv"): {\displaystyle {\displaystyle \pderiv{}{a} \HurwitzZeta@{s}{a} = -s \HurwitzZeta@{s+1}{a} }} .


Symbols List

& : logical and
 : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
 : sum : http://drmf.wmflabs.org/wiki/Definition:sum
 : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
 : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (10), Section 25.11 of DLMF.

URL links

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