Differential Polynomials
Properties of q shift difference differential polynomials of meromorphic functions
... For a transcendental meromorphic function f of finite order, herein and hereinafter, c is a nonzero complex constant and a(z) is small function with respect to f , Liu et al. [], Chen et al. [], and Luo and Lin [] ...
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Notes on the uniqueness of meromorphic functions concerning differential polynomials
... The uniqueness theory of meromorphic functions mainly studies conditions under which there is a unique function satisfying the given hypothesis. A great deal of classi- cal results in this field can be seen in [10], where ...
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Unicity of meromorphic functions and their linear differential polynomials
... 1 Introduction In , R Nevanlinna [–] proved his celebrated five-value and four-value theorems, which gave birth to the study of the unicity of meromorphic functions in the open comp[r] ...
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Normality of meromorphic functions and differential polynomials share values
... Yuan et al Advances in Difference Equations 2014, 2014 120 http //www advancesindifferenceequations com/content/2014/1/120 R ES EARCH Open Access Normality of meromorphic functions and differential po[.] ...
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Value distribution of q difference differential polynomials of entire functions
... Recently, the difference variant of the Nevanlinna theory has been established indepen- dently in [–]. Using these theories, value distributions of difference polynomials have been studied by many papers. For ...
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Normal Criteria and Shared Values by Differential Polynomials
... spherically uniformly on each compact subset of C, where g is a non-constant meromorphic function with order 2 , all of whose poles are ofmultiplicities at least 2, all of whose z[r] ...
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Uniqueness of Meromorphic Functions and Differential Polynomials
... We study the uniqueness of meromorphic functions and differential polynomials sharing one value with weight and prove two main theorems which generalize and improve some results earlier g[r] ...
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Value distribution of certain differential polynomials
... Lemma 2.6 (see [8]) . If P [f ] is as in Lemma 2.4, then T (r , P [f ]) = nT (r , f ) + S(r , f ). 3. The main result. In this section, we present the main result of the paper. Theorem 3.1 . Let f be a transcendental ...
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Generalization of Uniqueness Theorems for Entire and Meromorphic Functions
... It is well known that if f and g share four distinct values CM, then f is a fractional transformation of g. In 1997, corresponding to one famous question of Hayman, C. C. Yang and X. H. Hua showed the similar conclusions ...
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Vol 3, No 7 (2012)
... and differential monomials, differential polynomials generated by one of the ...non-constant differential polynomials and we denote by 𝑃𝑃 0 [𝑓𝑓] a differential polynomial not ...
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10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums
... sum (1.16) and the analogues of the expansions of hyperbolic cotangent and hy- perbolic tangent introduced in [20]. These results extend some known formulas [6, 7, 21]. We conclude this section by giving some identities ...
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On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions
... The Shifted Legendre polynomials are the special case of Shifted Jacobi polynomials and they can be obtained by p = q = 0, δ = 1 in the relation (2). We compared our technique with the existing methods ...
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Spectral Method for the Parabolic Inverse Problem Subject to Temperature Overspecification
... The existence and uniqueness and continuous dependence of the solutions to some kind of these inverse problems are discussed in [10,11,12,13]. The applications of these inverse problems and some other similar parameter ...
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Vol 6, No 8 (2015)
... partial differential equations can be cast into the Volterra integral equation ...partial differential equations, integral and integro-differential equations, stochastic equations and ...
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Numerical solution of gas solution in a fluid: fractional derivative model
... Müntz polynomials for solution of mathematical model of gas solution in a fluid is ...Müntz polynomials can ...Müntz polynomials reduces its numerical treatment to the solution of a linear system of ...
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Multivariable dimension polynomials and new invariants of differential field extensions
... In this paper, we introduce a special type of reduction in a ring of differential poly- nomials over a differential field of zero characteristic whose basic set is represented as a disjoint union of its subsets. Using the ...
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A Numerical Method For Solving Ricatti Differential Equations
... Riccati differential equation, we propose a weighted type of Adams- Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth ...
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Online Full Text
... Examples 1-3conveyedthe conclusion that the approach proposed in this paper could be effectively used to identify the numerical solution of the generalised variable order fractional partial differential equation. ...
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Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
... derivative polynomials, explicit formulas for the Bernoulli numbers and polynomials, for the Euler numbers and polynomials, for higher derivatives of some elementary functions, properties of the ...
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Numerical Solution of Fractional Order Delay Differential Equation using Shifted Chebyshev Polynomials of Second Kind
... Chebyshev Polynomials of second ...the polynomials defined in section ...chebyshev polynomials of second kind denoted by U n ∗ (x) for all x ∈ [0, 1] by change of variable s = 2x − 1 or x = 1/2(s + ...
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