Asymptotic Formula for the Moments of Takagi Function

Asymptotic Formula for the Moments of Takagi Function

Takagi function is a simple example of a continuous but nowhere diﬀerentiable function. It is deﬁned by T(x) = ∞ ᢘ k=0 2−nρ(2nx), where ρ(x) = min k∈Z |x − k|. The moments of Takagi function are deﬁned as Mn = ᝈ 1 0 xnT(x) dx. The main result of this paper is the following: Mn = lnn − Γ᝘(1) − lnπ n...

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Bibliographic Details
Main Author:	E. A. Timofeev
Format:	Article
Language:	English
Published:	Yaroslavl State University 2016-02-01
Series:	Modelirovanie i Analiz Informacionnyh Sistem
Subjects:	moments self-similar takagi function singular mellin transform asymptotic
Online Access:	https://www.mais-journal.ru/jour/article/view/302

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