The behavior of meromorphic solutions of differential equations has been the subject of much study. Research has concentrated on the value distribution of meromorphic solutions and their rates of growth. The purpose of the present paper is to show that a thorough search will yield a list of all meromorphic solutions of a multi-parameter ordinary differential equation introduced by Hayman. This ...

The generalized Stirling numbers introduced recently [11, 12] are considered in detail for the particular case s = 2 corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related q-polynomial identities are derived.

We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is CP1 and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of ...

ABSTRACT. The second fundamental theorem of Nevanlinna concerning meromorphic functions of a complex variable is extended in this note to an analogous result for meromorphic minimal surfaces. A similar extension of the first fundamental theorem involved generalizations of the classical proximity and enumerative functions and also a new visibility function; for the present result, a second enume...

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.

In this paper, we investigate the iterated order of meromorphic solutions of homogeneous and nonhomogeneous linear differential equations where the coefficients are meromorphic functions satisfying certain growth conditions. And some estimates of iterated convergence exponent are also given. 2000 Mathematics Subject Classification: 34M10, 30D35

Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan √ 8 ≈ 7032 . If in addition all critical points of the function are multiple, then a similar statement holds with π/2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f (k) + A(z)f = 0, k ≥ 2, where A(z) is a transcendental meromorphic function with ρp(A) = ρ > 0 and meromorphic functions of finite iterated p−order.

The purpose of the present paper is to introduce new classes of meromorphic spiral-like functions de…ned by using a meromorphic analogue of the Choi-Saigo-Srivastava operator for the generalized hypergeometric function and investigate a number of inclusion relationships of these classes.