关于和狄利克雷函数族作为广义马修级数的生成器，给出了近似和界

IF 0.5 Q3 MATHEMATICS Facta Universitatis-Series Mathematics and Informatics Pub Date : 2022-08-06 DOI:10.22190/fumi210519018c

P. Cerone

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引用次数: 1

摘要

积分表示广义马蒂厄系列和它的同伴被用来进行分析，导致新的见解Zeta和狄利克雷β函数族。利用Zeta和Dirichlet族边界的锐界得到边界，利用广义Mathieu级数结果的积分表示得到近似边界，特别是利用hardy型上界。

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ON ZETA AND DIRICHLET BETA FUNCTION FAMILIES AS GENERATORS OF GENERALIZED MATHIEU SERIES, PROVIDING APPROXIMATION AND BOUNDS

Integral representations for a generalized Mathieu series and its companions are used to undertake analysis leading to novel insights for Zeta and Dirichlet Beta function families. The bounds are procured using sharp bounds of Zeta and Dirichlet family bounds to procure approximating and bounds utilising integral representation of generalized Mathieu series results using in particular Hardy-type upper bounds.

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Facta Universitatis-Series Mathematics and Informatics MATHEMATICS-

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