Formula:DLMF:25.11:E45

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HurwitzZeta'@{-2}{a} - \frac{1}{12} a + \frac{1}{9} a^3 - \left( \frac{1}{6} a - \frac{1}{2} a^2 + \frac{1}{3} a^3 \right) \ln@@{a} \sim \sum_{k=1}^\infty \frac{2\!\BernoulliB{2k+2}}{(2k+2)(2k+1)2k(2k-1)} a^{-(2k-1)} }}

Note(s)

primes on Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \HurwitzZeta}} denote derivatives with respect to Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle s}}


Proof

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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 \mathrm{ln}}}  : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
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

Bibliography

Equation (45), Section 25.11 of DLMF.

URL links

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