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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 5, Pages 49–78 (Mi izv210)  

This article is cited in 5 scientific papers (total in 5 papers)

Regularity of infinite exponentials

A. P. Bulanov

Obninsk State Technical University for Nuclear Power Engineering

Abstract: If a sequence $\{a_k\}_{k=0}^{\infty}$ is such that $a_k\ne 0$, $k=0,1,2,…$, and $\varlimsup_{n\to\infty}|a_n|=\bar a<\infty$, then
$$ f(z)=\lim_{n\to\infty}a_0z^{a_1z^{a_2z\cdots^{a_{n-1}z^{a_n}}}} $$
is regular in a domain $U$ such that $D\cap e^K\subset U$, where $D=ż\colon|\arg z|<\pi\}$ and $e^K$ is the image of $K=\{w:|w|<\dfrac {1}{e\bar a}\}$ under the map $z=e^w$.

DOI: https://doi.org/10.4213/im210

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English version:
Izvestiya: Mathematics, 1998, 62:5, 901–928

Bibliographic databases:

MSC: 41A30, 30E10
Received: 04.10.1996

Citation: A. P. Bulanov, “Regularity of infinite exponentials”, Izv. RAN. Ser. Mat., 62:5 (1998), 49–78; Izv. Math., 62:5 (1998), 901–928

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. P. Bulanov, “Infinite iterated power with alternating coefficients”, Sb. Math., 192:11 (2001), 1589–1620  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. G. A. Ambartsumian, A. V. Burobin, “Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents”, Math. Notes, 73:2 (2003), 155–162  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. P. Bulanov, “Iterated cyclic exponentials and power functions with extra-periodic first coefficients”, Sb. Math., 201:1 (2010), 23–55  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. P. Bulanov, “O vozmozhnykh invariantakh na sovokupnosti pokazatelei vzaimno-obratnykh tsepnykh eksponent”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:4 (2015), 383–391  mathnet  crossref  elib
    5. Bulanov A.P., “Decomposition of Sum in Recurrent Formula For Exponents of the Inverse Chain Exponential”, Lobachevskii J. Math., 39:6 (2018), 747–754  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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