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- Dirichlet_eta_function abstract "In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0:This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted ζ*(s). The following simple relation holds: While the Dirichlet series expansion for the eta function is convergent only for any complex number s with real part > 0, it is Abel summable for any complex number. This serves to define the eta function as an entire function (and the above relation then shows the zeta function is meromorphic with a simple pole at s = 1, and perhaps poles at the other zeros of the factor ).Equivalently, we may begin by definingwhich is also defined in the region of positive real part. This gives the eta function as a Mellin transform.Hardy gave a simple proof of the functional equation for the eta function, which isFrom this, one immediately has the functional equation of the zeta function also, as well as another means to extend the definition of eta to the entire complex plane.".
- Dirichlet_eta_function thumbnail Complex_Dirichlet_eta_function.jpg?width=300.
- Dirichlet_eta_function wikiPageExternalLink zetaevaluations.pdf.
- Dirichlet_eta_function wikiPageExternalLink P155.pdf.
- Dirichlet_eta_function wikiPageID "447035".
- Dirichlet_eta_function wikiPageRevisionID "592374139".
- Dirichlet_eta_function hasPhotoCollection Dirichlet_eta_function.
- Dirichlet_eta_function title "Direct proof of eta = 0 by Sondow".
- Dirichlet_eta_function title "Indirect proof of eta = 0 following Widder".
- Dirichlet_eta_function titlestyle "background:palegreen;".
- Dirichlet_eta_function subject Category:Zeta_and_L-functions.
- Dirichlet_eta_function comment "In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0:This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted ζ*(s).".
- Dirichlet_eta_function label "Dirichlet eta function".
- Dirichlet_eta_function label "Dirichlet-èta-functie".
- Dirichlet_eta_function label "Dirichletsche η-Funktion".
- Dirichlet_eta_function label "Fonction êta de Dirichlet".
- Dirichlet_eta_function label "Función eta de Dirichlet".
- Dirichlet_eta_function label "Funkcja η".
- Dirichlet_eta_function label "Funzione eta di Dirichlet".
- Dirichlet_eta_function label "Função eta de Dirichlet".
- Dirichlet_eta_function label "دالة إيتا لديريشلت".
- Dirichlet_eta_function label "狄利克雷η函数".
- Dirichlet_eta_function sameAs Dirichletsche_η-Funktion.
- Dirichlet_eta_function sameAs Función_eta_de_Dirichlet.
- Dirichlet_eta_function sameAs Fonction_êta_de_Dirichlet.
- Dirichlet_eta_function sameAs Funzione_eta_di_Dirichlet.
- Dirichlet_eta_function sameAs Dirichlet-èta-functie.
- Dirichlet_eta_function sameAs Funkcja_η.
- Dirichlet_eta_function sameAs Função_eta_de_Dirichlet.
- Dirichlet_eta_function sameAs m.029jbf.
- Dirichlet_eta_function sameAs Q973313.
- Dirichlet_eta_function sameAs Q973313.
- Dirichlet_eta_function wasDerivedFrom Dirichlet_eta_function?oldid=592374139.
- Dirichlet_eta_function depiction Complex_Dirichlet_eta_function.jpg.
- Dirichlet_eta_function isPrimaryTopicOf Dirichlet_eta_function.
