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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Journal of Applied M...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Journal of Applied Mathematics and Computing
Article . 2006 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2006
Data sources: zbMATH Open
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A numerical investigation on the zeros of the Genocchi polynomials

Authors: Ryoo, C. S.;

A numerical investigation on the zeros of the Genocchi polynomials

Abstract

The author studies zeros of Genocchi polynomials. Genocchi polynomials \(G_n(x)\) are defined by the generating function as \[ {2t\over e^t+ 1} e^{xt}= \sum^\infty_{n=0} G_n(x){t^n\over n!}, \] and the Genocchi number \(G_n\) is defined by \(G_n= G_n(0)\). These are closely related to Euler polynomials and Euler numbers from their definitions. In Section 2, first the graphs of \(G_n(x)\) are given for \(1\leq n\leq 10\) and \(-3\leq x\leq 3\). And then zeros of \(G_n(x)\) for \(n=10\), \(20\), \(30\), \(40\) are plotted in the complex plane. These approximate numerical zeros are computed by Mathematica software. From that he observes the regular structure of the complex roots of \(G_n(x)\). In Section 3, he lists several open questions.

Related Organizations
Keywords

Genocchi polynomial, Euler number, Euler polynomial, Zeta functions and \(L\)-functions, Bernoulli and Euler numbers and polynomials, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), numerical experiments, Genocchi number

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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