ENTIRE FUNCTION
Growth of solutions to higher-order linear differential equations with entire coefficients
... are entire functions (6≡ 0) and a 1 , a 2 , d j are complex numbers (6= 0), and b j are real ...an entire function (6≡ 0) and of order σ(ϕ) < 1, while the solution f of the differential equation ...
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Order, type and cotype of growth for p-adic entire functions
... In complex analysis, it is known that if an entire function f has order t < +∞, then f and f 0 have same type. We will check that it is the same here. Theorems 14, 15, 16 are proven in [3]. Theorem 14: ...
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Growth of p-adic entire functions and applications
... Here we mean to introduce and study the notion of order of growth and type of growth for functions of order t. We will also introduce a new notion of cotype of growth in relation with the distribution of zeros in disks ...
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Results on Shared Values of Entire Functions and their Homogeneous Differential Polynomials
... nonconstant entire function such that µ (f ) < ∞, and let a be a nonzero complex ...nonconstant entire function f share a small entire function a with their derivative f (k) ...
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Complex and p-adic branched functions and growth of entire functions
... f . Moreover, if f ∈ A(K) \ K[x] (resp. let f ∈ A u (d(0, R − ))) then there exists at most two small functions w ∈ A f (K) (resp. w ∈ A f (d(0, R − ))) that are perfectly branched with respect to f . The next theorems ...
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On the growth of solutions of some second order linear differential equations with entire coefficients
... 1 Introduction and statement of results Throughout this paper, we assume that the reader is familiar with the funda- mental results and the standard notations of the Nevanlinna’s value distribu- tion theory (see [8], ...
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Entire functions sharing small functions with their difference operators
... Faculty of Exact Sciences, University of Bechar-(Algeria) elfarissi.abdallah@yahoo.fr Abstract. We investigate uniqueness problems for an entire function that shares two small functions of finite order with ...
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On the growth of solutions of some higher order linear differential equations with entire coefficients
... 6 |z| (k−j)(σ+ε) . (2.3) Lemma 2.2 ([3]) Suppose that P (z) = (α + iβ) z n + ... (α, β are real num- bers, |α| + |β| 6= 0) is a polynomial with degree n > 1, that A (z) (6≡ 0) is an entire function with ...
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Orders of solutions of an-th order linear differential equation with entire coefficients.
... as z → ∞ with Φ k ≤ arg z ≤ θ k for k = 1, ..., m and where A 0 (z) is tran - s cendental with ρ(A 0 ) < π/µ. Then every s o lution f 6≡ 0 of ( 1 . 1 ) has infinite o rder . Next , we provide a lemma that is used in ...
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Complex and p-adic branched functions and growth of entire functions
... meromorphic function admits at most two quasi- exceptional values and four perfectly branched values ...An entire function admits at most one quasi-exceptional value and two perfectly branched values ...
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Growth of solutions of linear differential equations with entire coefficients
... there exists a set E 8 ⊂ (1, ∞) that has finite logarithmic measure, such that (2.21) exp −r σ+ε 6 |f (z)| 6 exp r σ+ε holds for |z| = r / ∈ [0, 1] ∪ E 8 , r → +∞. Lemma 2.8 (see [16]). Let f (z) be an entire ...
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Iterated order of solutions of linear differential equations with entire coefficients
... order. Let n ≥ 2 be an integer and consider the linear differential equation A n (z) f (n) + A n−1 (z) f (n−1) + ... + A 1 (z) f ′ + A 0 (z) f = 0. (1.12) It is well-known that if A n ≡ 1, then all solutions of this ...
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Orders of solutions of an n-th order linear differential equation with entire coefficients
... (1.1) is an entire function with finite rational order; see for example [3], [5, pp. 199-209], [6, pp. 106-108], and [7, pp. 65-67]. ∗ Mathematics Subject Classifications: 30D35, 34M10, 34C10, 34C11. Key ...
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Order and hyper-order of entire solutions of linear differential equations with entire coefficients.
... EJDE – 2003 / 1 7 Benharrat Bela ¨ı di & Karima Hamani 5 2 Preliminary Lemmas We need the following lemmas for the proofs of our theorems . Lemma 2 . 1 ( [ 4 , p . 89 ] ) Let w be a transcendental entire ...
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Entire functions that share a small function with their difference operators
... an entire function f shares two distinct complex numbers CM with its derivative f 0 , then f ≡ f 0 ...meromorphic function f , if f , f 0 and f 00 share a finite nonzero value CM, then f 0 ≡ f ...
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Growth of certain combinations of entire solutions of higher order linear differential equations
... an entire function with ρ (f ) = α ≤ ∞, and let L (f) = a k f (k) + a k −1 f (k −1) + · · · + a 0 f, where a 0 , a 1 , · · · , a k are entire functions which are not all equal zero and satisfy b = ...
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On The Problem Of Entire Functions That Share a Small Function With Their Difference Operators
... ∆ c f (z) = f (z + c) − f (z) , ∆ n c f (z) = ∆ n−1 c (∆ c f (z)) , n ∈ N, n ≥ 2. In particular, ∆ n c f (z) = ∆ n f (z) for the case c = 1. Let f and g be two meromorphic functions and let a be a finite nonzero value. ...
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Growth of solutions of an n-th order linear differential equation with entire coefficients
... In the proof of Theorem 2.1, we need the following lemma: Lemma 2.4 ([4, p. 89]). Let w be a transcendental entire function of finite order r. Let G ¼ fðk 1 ; j 1 Þ; ðk 2 ; j 2 Þ; . . . ; ðk m ; j m Þg ...
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Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions
... We assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory of meromorphic functions ( see ([5])). Let σ (f ) denote the order of the growth ...
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Dynamic Function Specialization
... return c; 1) Analyzing and Monitoring phase: The first step in this phase is to find out the suitable ‘hot’ functions for specialization. The hot functions in the application can be determined by monitoring the spots ...
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