Geodesic
Asymptotics of the Basis Functions of Generalized Taylor Series for the Class $H_{\rho,2}$
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 738-754

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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. 
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     author = {V. A. Makarichev},
     title = {Asymptotics of the {Basis} {Functions} of {Generalized} {Taylor} {Series} for the {Class} $H_{\rho,2}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {738--754},
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     volume = {89},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a8/}
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V. A. Makarichev. Asymptotics of the Basis Functions of Generalized Taylor Series for the Class $H_{\rho,2}$. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 738-754. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a8/