Approximation of Analytic Functions by Kummer Functions [PDF]
Journal of Inequalities and Applications, 2010 We solve the inhomogeneous Kummer differential equation of the form xy′′+(β-x)y′-αy=∑m=0∞amxm and apply this result to the proof of a local Hyers-Ulam stability of the Kummer differential equation ...
Soon-Mo Jung
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Approximation of Analytic Functions by Chebyshev Functions [PDF]
Abstract and Applied Analysis, 2011 We solve the inhomogeneous Chebyshev's differential equation and apply this result for approximating analytic functions by the Chebyshev functions.
Soon-Mo Jung, Themistocles M. Rassias
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Joint Approximation of Analytic Functions by Shifts of Lerch Zeta-Functions
Mathematics, 2023 In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters.
Antanas Laurinčikas +2 more
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Approximation of Analytic Functions by Bessel's Functions of Fractional Order [PDF]
Abstract and Applied Analysis, 2011 We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by ...
Soon-Mo Jung
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On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function
Mathematics, 2022 The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a
Audronė Rimkevičienė +1 more
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Approximation of Analytic Functions by Shifts of Certain Compositions
Mathematics, 2021 In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions.
Darius Šiaučiūnas +2 more
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Approximation by Sequence of Operators Involving Analytic Functions
Mathematics, 2019 In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived.
Sezgin Sucu, Serhan Varma
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On approximation of analytic functions by periodic Hurwitz zeta-functions
Mathematical Modelling and Analysis, 2019 The periodic Hurwitz zeta-function ζ(s, α; a), s = σ +it, with parameter 0 < α ≤ 1 and periodic sequence of complex numbers a = {am } is defined, for σ > 1, by series sum from m=0 to ∞ am / (m+α)s, and can be continued moromorphically to the whole ...
Violeta Franckevič +2 more
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On tensor product approximation of analytic functions
Journal of Approximation Theory, 2016 Let \(T>0\), \(\mathbf{a}\in\mathbb{R}_{+}^{d}\), and \(\mathcal{D}_{\mathbf{a}} (T) = \{ \mathbf{k}\in\mathbb{N}_{0}^{d} : \sum_{j=1}^{d} a_j k_j \leq T \}\). The paper contains matching upper and lower asymptotic bounds with explicit constants for sums of the form \(\sum_{ \mathbf{k}\in\mathbb{N}_{0}^{d} \setminus \mathcal{D}_{\mathbf{a}} (T) } \exp \
Michael Griebel
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Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients
Mathematics, 2023 Let a={am:m∈N} be a periodic multiplicative sequence of complex numbers and L(s;a), s=σ+it a Dirichlet series with coefficients am. In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 ...
Darius Šiaučiūnas, Monika Tekorė
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