generalized series of Schlomilch

The concept of generalized series in a Banach space is introduced,convergence of the series is discussed,and some conditions under which a generalized series is convergent and some properties on the series are given.

研究了Ｂａｎａｃｈ空间中广义级数的收敛性，给出了广义级数收敛的等价条件及一系列判别方法；同时还得到了收敛广义级数的若干性质，并讨论了广义级数与普通级数的关

A necessary and sufficient condition is given for the existence of an entire function, being not identical to zero, bounded in a horizontal strip and represented by generalized Dirichlet series.

对于由广义Dirichlet级数表示,并且在固定带形有界、不恒为零的整函数的存在性,给出了充要条件。

For an entire functions represented by generalized Dirichlet series,the accurate zero order k(σ),type τ and infinite(R-H) order ρ(σ) in any horizontal line are defined and estimated.

对于由广义Dirichlet级数所表示的整函数f(s),引进它在每一条水平直线上的准确零(R)级k(σ)及型τL和无穷(R-H)级ρ(σ),得到关于它们的估计。

First,a complex shift value is added into governing equations,and a modal iterative formula is obtained with a generalized power series.

首先对控制方程进行移频处理,利用广义幂级数展开式获得模态迭代公式,并利用迭代结果与各阶振型表示复振型导数;然后把系统的广义动柔度矩阵表示为已知的低阶模态与截断的高阶模态之和,高阶模态部分采用多个矩阵多项式与一个广义幂级数的乘积表示,并利用系统的低阶模态和系统矩阵进行计算;各阶移频值表示为相应的移频系数与复特征值的乘积,它们仅与最低阶模态移频值的模和本阶模态的单位复特征值有关,而最低阶模态的移频系数通过精度分析获得。

Growth of the Generalized Dirichlet Series

广义Dirichlet级数的增长性

The Dirichlet Series and Random Dirichlet Series of Zero Order

零级Dirichlet级数与随机Dirichlet级数

The growth of Dirichlet series and random Dirichlet series of zero order

零级Dirichlet级数及随机Dirichlet级数的增长性

The Growth of Dirichlet Series and Random Dirichlet Series

Dirichlet级数和随机Dirichlet级数的增长性

Generalizations of Dirichlet Convergence Criteria in Series;

关于级数收敛的狄里克雷(Dirichlet)判别法的一些推广

The Growth of Dirichlet Series of Zero Order;

零级Dirichlet级数的增长性

The B-Valued Dirichlet Series of Infinite Order

无限级B-值Dirichlet级数

The Type of the Proximate Order of Dirichlet Series and Random Dirichlet Series of Finite Order

有限级Dirichlet级数及随机Dirichlet级数(R)准确级的型

The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane

半平面上无限级Dirichlet级数与随机Dirichlet级数的增长性

The Analytic Properties of a Dirichlet Series;

一类Dirichlet级数的解析性质

ON RANDOM DIRICHLET SERIES OF NONEQUALLY DISTRIBUTED;

非同分布随机Dirichlet级数

The Growth of Double Dirichlet Series

二重Dirichlet级数的增长性

Some Property of Random Dirichlet Series and B-Valued Random Dirichlet Series;

随机Dirichlet级数和B-值随机Dirichlet级数的一些性质

The Hyper-order of Dirichlet Series of Infinite Order in the Half Plane;

半平面上无限级Dirichlet级数的超级

THE ORDER AND THE LOW ORDER OF DIRICHLET SERIES OF INFINITE ORDER ON THE HALF PLANE

半平面上无限级Dirichlet级数的上下级

The Hyper-order of Random Dirichlet Series of Infinite Order in the Plane

平面上无限级随机Dirichlet级数的超级

The Growth of Random Dirichlet Series of Zero Order in the Half Plane;

半平面上零级随机Dirichlet级数的增长性

On the Borei lines of Dirichlet series of infinite order in the plane;

平面上无穷级Dirichlet级数的Borel线