ON THE GROWTH OF ENTIRE FUNCTIONS OF FINITE ORDER WITH DENSITY CONDITIONS

1966 ◽  
Vol 17 (1) ◽  
pp. 22-30 ◽  
Author(s):  
T. KÓVARI
Keyword(s):  
Finite Order ◽  
Entire Functions ◽  
Growth Of Entire Functions

scholarly journals The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wen Ju Tang ◽  
Jian Chen ◽  
Hong Yan Xu
Keyword(s):  
Finite Order ◽  
Complex Plane ◽  
Infinite Order ◽  
Entire Functions ◽  
Growth Order ◽  
Stieltjes Transform ◽  
Proximate Order ◽  
Growth Of Entire Functions ◽  
Stieltjes Transforms

In this article, we discuss the growth of entire functions represented by Laplace–Stieltjes transform converges on the whole complex plane and obtain some equivalence conditions about proximate growth of Laplace–Stieltjes transforms with finite order and infinite order. In addition, we also investigate the approximation of Laplace–Stieltjes transform with the proximate order and obtain some results containing the proximate growth order, the error, An∗, and λn, which are the extension and improvement of the previous theorems given by Luo and Kong and Singhal and Srivastava.

Algebraic Values of Entire Functions with Extremal Growth Orders: An Extension of a Theorem of Boxall and Jones

2019 ◽  
Vol 63 (3) ◽  
pp. 536-546
Author(s):  
Taboka Prince Chalebgwa
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Lower Order ◽  
Entire Functions ◽  
Compact Sets ◽  
Bounded Degree ◽  
Growth Of Entire Functions ◽  
Original Theorem

AbstractGiven an entire function $f$ of finite order $\unicode[STIX]{x1D70C}$ and positive lower order $\unicode[STIX]{x1D706}$, Boxall and Jones proved a bound of the form $C(\log H)^{\unicode[STIX]{x1D702}(\unicode[STIX]{x1D706},\unicode[STIX]{x1D70C})}$ for the density of algebraic points of bounded degree and height at most $H$ on the restrictions to compact sets of the graph of $f$. The constant $C$ and exponent $\unicode[STIX]{x1D702}$ are effectively computable from certain data associated with the function. In this followup note, using different measures of the growth of entire functions, we obtain similar bounds for other classes of functions to which the original theorem does not apply.

A note on meromorphic functions with finite order and of bounded l-index

2021 ◽  
Vol 18 (1) ◽  
pp. 1-11
Author(s):  
Andriy Bandura
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Finite Order ◽  
General Problem ◽  
Meromorphic Functions ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Meromorphic Solutions ◽  
Entire Solutions ◽  
Riccati Differential Equation

We present a generalization of concept of bounded $l$-index for meromorphic functions of finite order. Using known results for entire functions of bounded $l$-index we obtain similar propositions for meromorphic functions. There are presented analogs of Hayman's theorem and logarithmic criterion for this class. The propositions are widely used to investigate $l$-index boundedness of entire solutions of differential equations. Taking this into account we raise a general problem of generalization of some results from theory of entire functions of bounded $l$-index by meromorphic functions of finite order and their applications to meromorphic solutions of differential equations. There are deduced sufficient conditions providing $l$-index boundedness of meromoprhic solutions of finite order for the Riccati differential equation. Also we proved that the Weierstrass $\wp$-function has bounded $l$-index with $l(z)=|z|.$

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