ON THE DOMAIN OF THE CONVERGENCE OF TAYLOR-DIRECHLET SERIES WITH COMPLEX EXPONENTS

Authors

  • Andriy Kuryliak Ivan Franko National University of Lviv, Lviv, Ukraine
  • Mariia Kuryliak Ivan Franko National University of Lviv, Lviv, Ukraine
  • Oleh Skaskiv Ivan Franko National University of Lviv, Lviv, Ukraine

DOI:

https://doi.org/10.31471/2304-7399-2023-18(68)-25-31

Keywords:

Taylor-Dirichlet series; abscissa of the existence of maximal term

Abstract

The article deals with Dirichlet series of the form F(z) = Σ+∞ k=0 akezλk , as well as Taylor-Dirichlet series of the form F1(z) =+∞Σk=0 zmkakezλk , where (λk) is some sequence of pairwise different complex numbers, and mk is a sequence of non-negative integers, ak ∈ C. The main statements of the work are Statements 1–3 and relate to the description and relationship between the domains of convergence, absolute convergence, and the domains of existence of the maximum term of the above series F and F1.

References

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M.R. Kuryliak, O.B. Skaskiv, On the domain of convergence of general Dirichlet series with complex exponents, Carpathian Math. Publ., (2023) (submitted)

М.Р. Куриляк, О.Б. Скаскiв, Випадковi банахово-значнi ряди Дiрiхле зi зростаючою детермiнованою послiдовнiстю додатних показникiв, Прикарпатський вiсник НТШ. Число, 2022, No 17(64), 9–20. https://doi.org/10.31471/2304-7399-2022-17(64)-9-21

Published

2023-12-01

How to Cite

Kuryliak, A., Kuryliak, M., & Skaskiv, O. (2023). ON THE DOMAIN OF THE CONVERGENCE OF TAYLOR-DIRECHLET SERIES WITH COMPLEX EXPONENTS. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY Number, (18(68), 25–31. https://doi.org/10.31471/2304-7399-2023-18(68)-25-31