Symmetric identities of higher-order degenerate q-Bernoulli polynomials
The purpose of this paper is to give symmetric identities for higher-order degenerate q- Bernoulli polynomials arising from the p-adic q-integral on Zp.
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arXiv subjects
Taekyun Kim
Publications and source records attributed to Taekyun Kim.
Convolved Fibonacci Numbers and their applications
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.
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Symmetric identities for an analogue of Catalan polynomials
In this paper, we consider an analogue of Catalan polynomials and give some identities of symmetry for those polynomials by using fermionic $p$-adic integrals on the ring of $p$-adic integers
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A note on Catalan numbers associated with p-adic integral on Zp
In this paper, we study Catalan numbers which can be represented by the p-adic integral on Zp and we investigate some properties and formulae related to Catalan numbers and special numbers.
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A new approach to Catalan numbers using differential equations
In this paper, we introduce two differential equations arising from the generating function of the Catalan numbers which are `inverses' to each other in some sense. From these differential equations, we obtain some new and explicit identities for Catalan and higher-order Catalan numbers. In addition, by other means than differential equations we also derive some interesting identities involving Catalan numbers which are of arithmetic and combinatorial nature.
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Differential equations associated with Lambda-Changhee polynomials
In this paper, we study linear differential equations arising from $λ$- Changhee polynomials (or called degenerate Changhee polynomials) and give some explicit and new identities for the $λ$-Changhee polynomials associated with linear differential equations.
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Nonlinear differential equation for Korobov numbers
In this paper, we present nonlinear differential equations for the generating functions for the Korobov numbers and for the Frobenuius-Euler numbers. As an application, we find an explicit expression for the nth derivative of 1/ log(1 + t).
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Nonlinear differential equations arising from Boole numbers and their applications
In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising from our nonlinear differential equations.
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Some identities of Eulerian polynomials arising from nonlinear differential equations
In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and higher-order Eulerian polynomials.
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Differential equations associated with Legendre polynomials
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre polynomials.
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Differential equations for Changhee polynomials and their applications
Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [7]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.
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Some identities of Chebyshev polynomials arising from nonlinear differential equations
In this paper, we investigate some properties of Chebyshev polynomials arising from non-linear differential equations. From our investigation, we derive some new and interesting identities on Chebyshev polynomials.
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A note on Hermite polynomials
In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.
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Identities involving Bessel polynomials arising from linear differential equations
In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
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Identities of symmetry for the generalized degenerate Euler polynomials
In this paper, we give some identities of symmetry for the generalized degenerate Euler polynomials attached to chi which are derived from the symmetric properties for certain fermionic p-adic integrals on Zp.
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Degenerate Euler zeta function
Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with degenerate Euler polynomials at negative integers.
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On degenerate Carlitz q-Bernoulli polynomials
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
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On the degenerate Forbenius-Euler polynomials
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
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