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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
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λ-q-Sheffer sequence and its applications
Demonstratio Mathematica, 2022 Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Fractional calculus, zeta functions and Shannon entropy
Open Mathematics, 2021 This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ\zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative.
Guariglia Emanuel
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Some identities related to degenerate Stirling numbers of the second kind
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Duality for convolution on subclasses of analytic functions and weighted integral operators
Demonstratio Mathematica, 2023 In this article, we investigate a class of analytic functions defined on the unit open disc U={z:∣z∣0\alpha \gt 0, 0≤β≤10\le \beta \le 1 ...
Amini Ebrahim +3 more
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Representations by degenerate Daehee polynomials
Open Mathematics, 2022 In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials.
Kim Taekyun +3 more
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Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials
Alexandria Engineering Journal, 2021 This work adopts to the time-fractional Klein–Gordon equation (FKGE) in the Caputo sense. We present a new technique using the clique polynomial as basis function for the operational matrices to obtain solution of time-FKGE.
R.M. Ganji +3 more
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Some identities on generalized harmonic numbers and generalized harmonic functions
Demonstratio Mathematica, 2023 The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms.
Kim Dae San, Kim Hyekyung, Kim Taekyun
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A study on the q-Euler numbers and the fermionic q-integrals of the product of several type $q$-Bernstein polynomials on Zp [PDF]
, 2003 In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.Comment: 7 ...
Kim, Taekyun
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 12, Page 599-605, 2004., 2004 We consider the modified q‐analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s), 0 < q < 1, s ∈ ℂ. In this paper, we give q‐Bernoulli numbers which can be viewed as interpolation of the above q‐analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at ...
Taekyun Kim
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