Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function

被引：0
作者：
Giedrius Alkauskas
机构：
[1] Universität für Bodenkultur Wien,Institute of Mathematics, Department of Integrative Biology
[2] Vilnius University,Faculty of Mathematics and Informatics
来源：
The Ramanujan Journal | 2011年 / 25卷
关键词：
The Minkowski question mark function; Moments of distribution; Periods; Bessel functions; Semi-regular continued fractions; The Farey tree; 11A55; 26A30; 33C10; 11F67;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper continues investigations on various integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it has a hidden nice interpretation in terms of semi-regular continued fractions. The proof is self-contained and does not rely on previous results by the author.
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页码：359 / 367
页数：8
相关论文
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