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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 738–754 (Mi mz8844)  

Asymptotics of the Basis Functions of Generalized Taylor Series for the Class $H_{\rho,2}$

V. A. Makarichev

National Aerospace University "Kharkiv Aviation Institute"

Abstract: We study the basis functions $\varphi_{n,k}$ and $\psi_{n,p}$ of generalized Taylor series for the class $H_{\rho,2}$ and obtain asymptotic expansions of the functions $\varphi^{(l)}_{n,0}$ and $\psi^{(l)}_{n,2\cdot4^n-1}$. We prove the existence of an asymptotics for the functions $\varphi_{n,k}$ and $\psi_{n,p}$ for $k\ne 0$ and $p\ne {2\cdot4^n}-1$. The first term of the asymptotic expansions of these functions is obtained.

Keywords: generalized Taylor series, basis functions, the class of functions $H_{\rho,2}$, functional-differential equation

DOI: https://doi.org/10.4213/mzm8844

Full text: PDF file (529 kB)
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English version:
Mathematical Notes, 2011, 89:5, 689–705

Bibliographic databases:

UDC: 517
Received: 29.04.2009
Revised: 06.09.2010

Citation: V. A. Makarichev, “Asymptotics of the Basis Functions of Generalized Taylor Series for the Class $H_{\rho,2}$”, Mat. Zametki, 89:5 (2011), 738–754; Math. Notes, 89:5 (2011), 689–705

Citation in format AMSBIB
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