It is concluded that the order of growth and convergence of the two kinds of bi-random Taylor series are the same.
研究两类双随机Taylor级数在满足一定条件下的收敛性,增长性之间的关系,得出了在一定条件下,两类双随机Taylor级数有几乎相同的收敛性和增[增长]级。
In this paper,the growth and of the random Taylor series in the plane are studied,and under certain conditions,comes the important results:the order of growth on a radius is the same as the plane a.
本文研究了全平面上的随机Taylor级数的增长性和收敛性,得出在一定条件下该级数沿任意半径上增[增长]级与单位圆内的增[增长]级相同。
Then it draws some conditions that the order of growth on a radius is the same as the unit ciricl
研究了单位圆内的随机Taylor级数的增长性和收敛性,认为沿任意半径上增[增长]级与单位圆内增[增长]级相同。
The Reasearch on Some Properties of growth order of mermorphic functions;
亚纯函数增[增长]级的性质进一步探讨
The relation between the solution to certain linear differential equation of higher order of certain entire function coefficient and small function is studied,obtaining a series of results,such as growth order,zero point,taking small function point.
对某类整函数系数的高阶线性微分方程解与小函数间的关系进行研究,得到了方程解的增[增长]级,零点,取小函数点的一系列结果,所得结果推广了一些相关结果。
In this paper,the growth orders of the solutions to the differential equation f(k)+Ak-1f(k-1)+.
讨论齐次线性微分方程f(k)+Ak-1f(k-1)+…+A0f=0,k≥2的解的增[增长]级,其中方程的系数为至多有限多个极点的亚纯函数,且不存在某个系数的级大于其他系数的级。
Under a given condition, we have gained the result that the order of growth on a line is the same as that on the right half plane.
研究了右半平面上的随机Dirichlet级数的增长性和收敛性,得出了在一定条件下,任何水平线上增[增长]级与右半平面上相同。
It is proved that if A(z) has order(2,1;ρ),then the order of growth of nontrivial solution is(3,1;ρ) and the equation always has a solution that the exponent of convergence of its zero-sequence is(3,1;ρ) too.
证明当A(z)的增[增长]级为(2,1;ρ)时,方程的每一个非平凡解的增[增长]级都为(3,1;ρ),而且总存在一个非平凡解f(z)的零点收敛级等于其增[增长]级(3,1;ρ)。
It is found that the stochastic Dirichlet series share common features with the non-random Dirichlet series in order of growth.
利用φ-混合序列推广的Borel-Cantelli引理及一些收敛定理,在条件EXn=0,α>0,0<2α2nσ=2αE|Xn|2≤E2|Xn|<∞下,研究系数为φ-混合序列的随机Dirichlet级数∞∑n=0Xn(ω)e-λns的增长性,得出其增[增长]级和非随机Dirichlet级数的增[增长]级有类似的性质。
This paper deals with the orders and zeros of the solutions of the differential equation f~((k))+A_(k-1)f~((k-1)).
本文研究了微分方程f~(k)+A_((k-1))f~((k-1))+…+A_0f=F(k≥2)解的增[增长]级和零点收敛指数,其中A_j=B_je~(P_j),j=0,1,…,k-1,B_j(z)为整函数,P_j(z)为多项式,σ(B_j)＜degP_j。
It is proved that every solution f of the above equation is of order 1 and hyper order a positive interger no greater than degQ.
研究非齐次线性微分方程f(k)+ak-1f(k-1)+…+a1f′-(eQ(z)-a0)f=1(k≥1)解的增长性,其中aj(j=0,1,…,k-1)为常数,Q(z)是非常数多项式,得出上述方程的有穷级解的增[增长]级为1,无穷级解的超级为不大于degQ的正整数。
In this paper, we investigate the orders and zeros of the solutions of the differ- ential equation where Ao,… , Ak-1, F are entire functions with finite orders, and Ao,….
在本文中假设微分方程的系数为有限级整函数且满足：对于每个不恒等于零的系数Ａｊ（ｊ为整数且 ），其零点收敛指数小于其增[增长]级，且当 的增[增长]级等于 Ａｉ与 Ａｊ增[增长]级的最大值，以及自由项Ｆ为有限级整函数。
In this paper,we study the growth of solution for a certain higher order differential equation: f (k) +(Q 1(z)e P 1(z) +Q 2(z)e P 2(z) )f=P 3(z), where P 1(z)=ζ 1z n+…,P 2(z)=ζ 2z n+…,P 3(z)0 are non constant polynomials,and Q 1(z),Q 2(z) are entire functions which have order less then n.
研究了k(≥ 2 )阶线性微分方程f(k) +(Q1(z)eP1(z) +Q2 (z)eP2 (z) )f=P3(z)的解的增[增长]级 ,其中P1(z) =ζ1zn+… ,P2 (z) =ζ2 zn+…为非常数多项式 ,P3(z)为非零多项式 ,Q1(z) ,Q2 (z)均为级小于n的整函数且不同时恒为零 。
In this paper,we investigate the iterated order and iterated convergence exponent to zero sequence of the solutions of some classes of differential equations.
本文研究了几类微分方程解的迭代增[增长]级及零点迭代收敛指数。