For Weierstrass functions σ(z) and ζ(z), we present the asymptotic formulas valid outside the efficiently constructed exceptional sets of discs that are much narrower than in the known asymptotic formulas.
References
A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 2, Nauka, Moscow (1968).
N. E. Korenkov, “On the distribution of values of the Weierstrass sigma-function,” Mat. Sb., No. 1, 240–242 (1976).
Yu. I. Lyubarskii and M. L. Sodin, Analogs of Functions of the Sine Type for Convex Domains [in Russian], Preprint, Institute for Low Temperature Physics and Engineering, Ukrainian Academy of Sciences, Kharkov (1986).
A. A. Gol’dberg and N. E. Korenkov, “Asymptotics of the logarithmic derivative of an entire function of completely regular growth,” Sib. Mat. Zh., 21, No. 3, 63–79 (1980).
A. A. Gol’dberg and N. E. Korenkov, “Asymptotic behavior of the logarithmic derivative of an entire function of completely regular growth,” Ukr. Mat. Zh., 30, No. 1, 25–32 (1978); English translation: Ukr. Math. J., 30, No. 1, 17–22 (1978).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 1, pp. 135–138, January, 2014.
Rights and permissions
About this article
Cite this article
Zając, J., Korenkov, M.E. & Kharkevych, Y.I. On the Asymptotics of Some Weierstrass Functions. Ukr Math J 67, 154–158 (2015). https://doi.org/10.1007/s11253-015-1070-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-015-1070-8