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mathematical analysis > calculus > series > rational zeta series

number > real number > rational zeta series

number > number theory > analytic number theory > L-function > rational zeta series

mathematical analysis > complex analysis > meromorphic function > L-function > rational zeta series

Preferred term

rational zeta series

Definition(s)

In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function. Specifically, given a real number x, the rational zeta series for x is given by

${\\displaystyle x=\\sum _{n=2}^{\\infty }q_{n}\\zeta (n,m)}$

where q_n is a rational number, the value m is held fixed, and ζ(s, m) is the Hurwitz zeta function. It is not hard to show that any real number x can be expanded in this way.

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

Broader concept(s)

Related concept(s)

In other languages

série zêta rationnelle

French

URI

http://data.loterre.fr/ark:/67375/PSR-NHDPQMVR-B

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