Treffer: asymptotics of the partial sums of a set of integral transforms: Asymptotics of the partial sums of a set of integral transforms
Title:
asymptotics of the partial sums of a set of integral transforms: Asymptotics of the partial sums of a set of integral transforms
Authors:
Source:
Numerical Algorithms. 25(1):279-291
Publisher Information:
Springer US, New York, NY, 2000.
Publication Year:
2000
Subject Terms:
asymptotics, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), zeros, Special classes of entire functions of one complex variable and growth estimates, integral transforms, Power series (including lacunary series) in one complex variable
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
ISSN:
1017-1398
DOI:
10.1023/a:1016681628636
Access URL:
Accession Number:
edsair.dedup.wf.002..b7960b43e7254e1855e779b53bda370a
Database:
OpenAIRE
Weitere Informationen
In the paper under review, the author investigates the asymptotic distribution of zeros of the partial sums of the family of entire functions defined by \[ G(z):=\int_0^1\mu (t) t^{\alpha-1}(1-t)^{\beta-1}e^{zt} dt, \] where \(\operatorname {Re} \alpha\), \(\operatorname {Re} \beta >0\), \(\mu\) is Riemann integrable on \([0,1]\), continuous at \(t=0,1\) and satisfies \(\mu (0)\mu (1)\neq 0\). In particular, the author demonstrates in this work that the limit curve of the collection of suitably normalized zeros of the partial sums is the same for the whole family of functions under consideration. The reviewer remarks that the computer generated graphs of the limit curves are truly impressive.