Borel的一个经典性定理是,如果两组整函数G_i(Z)(i=1,2,…,n)和H_i(Z)(i=1,2,…n)满足恒等式sum from j=1 to n G_i(Z)e^Hj^(Z)≡0 并且如果G_i(1≤i≤n)的增长性,在某种意义下,较慢于e^Hj^(-H)k(1≤j,k≤n,j≠k)的增长性,则G_i(Z)≡0 (...Borel的一个经典性定理是,如果两组整函数G_i(Z)(i=1,2,…,n)和H_i(Z)(i=1,2,…n)满足恒等式sum from j=1 to n G_i(Z)e^Hj^(Z)≡0 并且如果G_i(1≤i≤n)的增长性,在某种意义下,较慢于e^Hj^(-H)k(1≤j,k≤n,j≠k)的增长性,则G_i(Z)≡0 (i=1,2,…,n),在本文中得出了这个定理的几个推广。展开更多
In this paper meromorphic functions are always functions which are meromorphic for |z|<+∞.In the theory of meromorphic functions the importance of the second fundamental theorem:
Baker studied the growth of the comPosite function f{f(z)} for a transcendentally entire function f(z) of zero order and showed by three examples that the order of f{f(z)} can be O, ∞ or 1. In the present letter, we ...Baker studied the growth of the comPosite function f{f(z)} for a transcendentally entire function f(z) of zero order and showed by three examples that the order of f{f(z)} can be O, ∞ or 1. In the present letter, we give two sufficient conditions under which the function f{f(z)} is of zero order (or infinite order). Besides, making use of some results of Baker’s, we construct a transcendentally entire function f(z)展开更多
In former works, I proved the followingTheorem 1. Let f（x）, r（t） and δ（x） be three functions satisfying the following conditions: f（x） is non-decreasing and f（x）≥t0 for x≥x0; r（t） is positive,
This paper proves an inequality of the following form: where f(z) is a transcendental meromorphic function, F(z) denotes adifferential polynomial of f(z) of a certain general form, φ(z)0 means ameromorphic function s...This paper proves an inequality of the following form: where f(z) is a transcendental meromorphic function, F(z) denotes adifferential polynomial of f(z) of a certain general form, φ(z)0 means ameromorphic function such that T(r, φ)= S(r, f) and K signifies a positive constant.展开更多
文摘Borel的一个经典性定理是,如果两组整函数G_i(Z)(i=1,2,…,n)和H_i(Z)(i=1,2,…n)满足恒等式sum from j=1 to n G_i(Z)e^Hj^(Z)≡0 并且如果G_i(1≤i≤n)的增长性,在某种意义下,较慢于e^Hj^(-H)k(1≤j,k≤n,j≠k)的增长性,则G_i(Z)≡0 (i=1,2,…,n),在本文中得出了这个定理的几个推广。
文摘In this paper meromorphic functions are always functions which are meromorphic for |z|<+∞.In the theory of meromorphic functions the importance of the second fundamental theorem:
文摘Baker studied the growth of the comPosite function f{f(z)} for a transcendentally entire function f(z) of zero order and showed by three examples that the order of f{f(z)} can be O, ∞ or 1. In the present letter, we give two sufficient conditions under which the function f{f(z)} is of zero order (or infinite order). Besides, making use of some results of Baker’s, we construct a transcendentally entire function f(z)
文摘In former works, I proved the followingTheorem 1. Let f（x）, r（t） and δ（x） be three functions satisfying the following conditions: f（x） is non-decreasing and f（x）≥t0 for x≥x0; r（t） is positive,
基金Project supported by the National Natural Science Foundation of China.
文摘This paper proves an inequality of the following form: where f(z) is a transcendental meromorphic function, F(z) denotes adifferential polynomial of f(z) of a certain general form, φ(z)0 means ameromorphic function such that T(r, φ)= S(r, f) and K signifies a positive constant.
