نتایج جستجو برای: meromorphic function
تعداد نتایج: 1215101 فیلتر نتایج به سال:
In this paper, we give some necessary conditions for a complex difference equation of Malmquist type $$sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))},$$ where $n(in{mathbb{N}})geq{2}$, and $P(f(z))$ and $Q(f(z))$ are relatively prime polynomials in $f(z)$ with small functions as coefficients, admitting a meromorphic function of finite order. Moreover, the properties of finite o...
We investigate when differential polynomials in real transcendental meromorphic functions have non-real zeros. For example, we show that if g is a real transcendental meromorphic function, c ∈ R \ {0} and n ≥ 3 is an integer, then g′gn − c has infinitely many non-real zeros. If g has only finitely many poles, then this holds for n ≥ 2. Related results for rational functions g are also considered.
In the paper, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F , f ′ + af = b has at most one zero, where n is a positive integer, a and b = 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible.
1. Abelian functions by Poincaré. 1-1. If the variable x and a general solution y of a linear differential equation with polynomial coefficients are algebraically dependent, the periods of abelian integrals of the first kind associated with the curve f(x, y) = 0 satisfy certain relations. In his earliest works on abelian functions Poincaré examined such relations in some special cases. He also ...
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