Results 31 to 40 of about 6,158,527 (245)
ON THE UNIQUENESS OF ENTIRE FUNCTIONS
Bulletin of the Korean Mathematical Society, 2004 Summary: We study the uniqueness of entire functions and prove the following result: Let \(f(z)\) and \(g(z)\) be two nonconstant entire functions, \(n\geq 7\) a positive integer, and let \(a\) be a nonzero finite complex number. If \(f^n(z)(f(z)-1)f'(z)\) and \(g^n(z)(g(z)-1)g'(z)\) share \(a\) CM, then \(f(z)\equiv g(z)\).
Qiu, Huiling, Fang, Mingliang
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On the Zeta-Function of Zeros of Entire Function [PDF]
Journal of Siberian Federal University. Mathematics & Physics, 2021 This article is devoted to the study of the properties of the zeta-function of zeros of entire function. We obtained an explicit expression for the kernel of the integral representation of the zetafunction in one ...
Kuzovatov, Vyacheslav I. +2 more
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Singular values of two-parameter families λ((bz − 1)/z)μ and λ(z/(bz − 1))η
Journal of Taibah University for Science, 2017 The singular values of two kinds of two-parameter families of functions (i) fλ,μ(z)=λ((bz−1)/z)μ and fλ,μ(0) = λ(ln b)μ, μ > 0, (ii) gλ,η(z)=λ(z/(bz−1))η and gλ,η(0) = λ/(ln b)η, η > 0; λ∈ℝ∖{0}, z∈ℂ, b > 0, b ≠ 1 are described.
Mohammad Sajid
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Multiple interpolation with the fast-growing knots in the class of entire functions and its application [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 The conditions for the sequence of complex numbers (bn,k) are obtained, such that the interpolation problem g(k-1)(λn) = bn,k, k ∈ 1, s, n ∈ N, where |λk/λk+1| ≤ ∆ < 1, has a unique solution in some classes of entire functions g for which Mg(r) ≤ c1 exp (
I. Sheparovych
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Researches in Mathematics, 2019 Estimates above and estimates below have been obtained for Kolmogorov, linear and Bernshtein average $\nu$-widths on the classes of functions $W^r (\omega^w, \Psi)$, where $r \in \mathbb{N}$, $\omega^w(f)$ is the generalized characteristic of smoothness ...
S.B. Vakarchuk, M.B. Vakarchuk
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A new class of the entire function of order one: a case study [PDF]
, 2022 In this article, a new class of the entire function of order one, expressed by the series and product representations with the real positive coefficients and complex zeros, is investigated for the first time.
Yang, Xiao-Jun
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On properties of the solutions of the Weber equation
Karpatsʹkì Matematičnì Publìkacìï, 2015 Growth, convexity and the $l$-index boundedness of the functions $\alpha(z)$ and $\beta(z)$, such that $\alpha(z^4)$ and $z\beta(z^4)$ are linear independent solutions of the Weber equation $w''-(\frac{z^2}4-\nu-\frac12) w=0$ if $\nu=-\frac12$ are ...
Yu.S. Trukhan
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Approximation of functions from generalized Nikol’skii– Besov classes by entire functions in Lebesgue spaces(in Ukrainian) [PDF]
Математичні Студії, 2013 Exact-order estimates for the approximations of functions ofclasses $S^{Omega}_{p,{heta}}B(mathbb{R}^d)$ by entirefunctions with the spectrum of a special form in the space$L_q(mathbb{R}^d)$ for some relations between the parameters$p$ and $q$, are ...
V. V. Myroniuk, S. Ya. Yanchenko
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Uniqueness of Entire Functions
Annals of the Alexandru Ioan Cuza University - Mathematics, 2011 Uniqueness of Entire Functions In this paper, we study the uniqueness problems on meromorphic functions sharing a finite set. The results extend and improve some theorems obtained earlier by Fang (2002) and Zhang-Lin (2008).
Zhang, Yi, Xiong, Wei-Ling
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On the zeros of the derivatives of an entire function [PDF]
Proceedings of the American Mathematical Society, 1957 Let f(z) be an entire function. We define the point set L=Lf on the z-sphere as follows: zo0EL if and only if every neighborhood of zo contains zeros of infinitely many of the functions f(n)(z). In [3] Polya has named this set the final set of f, and collected various facts and conjectures about final sets. The object of this paper is to prove that any
Edrei, A., MacLane, G. R.
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