Formula:DLMF:25.11:E43

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HurwitzZeta@{s}{a} - \frac{a^{1-s}}{s-1} - \frac{1}{2} a^{-s} \sim \sum_{k=1}^{\infty} \frac{\BernoulliB{2k}}{(2k)!} \frac{\EulerGamma@{s+2k-1}}{\EulerGamma@{s}} a^{1-s-2k} }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle a \to \infty}} in the sector Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle |\ph@@{a}| \leq \cpi-\delta (<\cpi)}} , with Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle s (\neq 1)}} and Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta}} fixed


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

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \zeta}}  : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \tilde}}  : asymptotic equality : http://dlmf.nist.gov/2.1#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 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 \Gamma}}  : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{ph}}}  : phase : http://dlmf.nist.gov/1.9#E7
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \pi}}  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4

Bibliography

Equation (43), Section 25.11 of DLMF.

URL links

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