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Displaying similar documents to “On the growth of an algebroid function with radially distributed values”

Comparative growth analysis of Wronskians in the light of their relative orders

Sanjib Kumar Datta, Tanmay Biswas, Ahsanul Hoque (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.

Selected results of the theory of value distribution and growth of meromorphic functions

Ewa Ciechanowicz (2015)

Banach Center Publications

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The paper discusses development of the theory of value distribution and growth of meromorphic functions, focusing on two basic notions: exceptional values and asymptotic values. Some historical context is given and contemporary achievements are presented. In particular, recent results concerning exceptional functions and asymptotic functions are considered.

On meromorphic solutions of the Riccati differential equations

Ran Ran Zhang, Zong Xuan Chen (2010)

Annales Polonici Mathematici

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We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we...

Hyper-order and order of meromorphic functions sharing functions

Jianming Qi, Wenjun Yuan, Hongxun Yi (2015)

Annales Polonici Mathematici

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In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.

On a kth-order differential equation

Xiao-Min Li, Cun-Chen Gao (2006)

Annales Polonici Mathematici

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We prove a theorem on the growth of a solution of a kth-order linear differential equation. From this we obtain some uniqueness theorems. Our results improve several known results. Some examples show that the results are best possible.

Resolvent conditions and powers of operators

Olavi Nevanlinna (2001)

Studia Mathematica

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We discuss the relation between the growth of the resolvent near the unit circle and bounds for the powers of the operator. Resolvent conditions like those of Ritt and Kreiss are combined with growth conditions measuring the resolvent as a meromorphic function.

The growth of solutions of algebraic differential equations

Walter K. Hayman (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Suppose that f ⁢ z is a meromorphic or entire function satisfying P ⁢ z , f , f ′ , … , f n = 0 where P is a polynomial in all its arguments. Is there a limitation on the growth of f , as measured by its characteristic T ⁢ r , f ? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.