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mathematical physics > special function > Hurwitz zeta function

mathematical analysis > functional analysis > special function > Hurwitz zeta function

number > number theory > analytic number theory > L-function > Hurwitz zeta function

mathematical analysis > complex analysis > meromorphic function > L-function > Hurwitz zeta function

Preferred term

Hurwitz zeta function

Definition(s)

In mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables $s$ with $Re(s) > 1$ and $a \neq 0, -1, -2, \dots$ by

${\\displaystyle \\zeta (s,a)=\\sum _{n=0}^{\\infty }{\ rac {1}{(n+a)^{s}}}.}$

This series is absolutely convergent for the given values of $s$ and $a$ and can be extended to a meromorphic function defined for all $s \neq 1$ . The Riemann zeta function is $ζ(s,1)$ . The Hurwitz zeta function is named after Adolf Hurwitz, who introduced it in 1882.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hurwitz_zeta_function)

Broader concept(s)

Related concept(s)

In other languages

fonction zêta de Hurwitz

French

URI

http://data.loterre.fr/ark:/67375/PSR-T36RJ8T9-6

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