A note on q-analogue of Sandor's functions
The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. Sandor. In this note, we obtain q-analogue of Sandor's theorems.
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arXiv subjects
Taekyun Kim
Publications and source records attributed to Taekyun Kim.
$q$-Volkenborn Integration and Its Applications
The main purpose of this paper is to present a systemic study of some families of multiple $q$-Euler numbers and polynomials. In particular, by using the $q$-Volkenborn integration on $\Bbb Z_p$, we construct $p$-adic $q$-Euler numbers and polynomials of higher order. We also define new generating functions of multiple $q$-Euler numbers and polynomials. Furthermore, we construct Euler $q$-Zeta function. This paper is the version of the preprint of my paper to publish in the special issues as the preprint part of this proceedings.
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On the alternating sums of powers of consecutive q-integers
In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.
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q-Euler and Genocchi numbers
Carlitz has introduced an interesting $q$-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the $q$-Euler numbers. In this paper we give another construction of $q$-Euler numbers, which are different than his $q$-Euler numbers. By using our $q$-Euler numbers, we define the $q$-analogue of Genocchi numbers and investigate the relations between $q$-Euler numbers and $q$-analogs of Genocchi numbers.
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A note on multiple Dirichlet's q-L--function
Recently, the two variable $q$-$L$-functions which interpolate the generalized $q$-Bernoulli polynomials associated with $χ$ are introduced and studied, cf. [2]. In this paper, we construct multiple Dirichlet's $q$-$L$-function which interpolates the generalized multiple $q$-Bernoulli numbers attached to $χ$ at negative integer and study its properties.
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Multivariate p-dic L-function
We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.
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An analogue of Lebesgue-Radon-Nikodym theorem with respect to p-adic q-invariant distribution on $\Bbb Z_p$
The purpose of this paper is to derive the analogue of Lebesgue-Radon-Nikodym theorem with respect to $p$-adic $q$-invariant distribution on $\Bbb Z_p$ which is defined by author in [1].
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On a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and Its derivative
We construct the q-extension of the Hurwitz's type L-function which interpolates the q-extension of generalized Bernoulli polynomials attached to $chi$.
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On the explicit formula of Euler numbers and polynomials of higher order
We study the explicit formula of Euler numbers and polynomials of higher order
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A note on q-Bernoulli numbers and polynomials
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.
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On the twisted $q$-zeta functions and $q$-Bernoulli polynomials
We study the twisted q-zeta functions and twisted q-Bernoulli polynomials
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Barnes' type multiple Changhee q-zeta functiond
We construct Barnes' type Changhee q-zeta function.
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q-analogue of Euler-Barnes' numbers and polynomials
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
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q-analogues of the sums of powers of consecutive integers
Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.
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On the q-analogue of two-variable p-adic L-function
We construct the two-variable $p$-adic $q$-$L$-function which interpolates the generalized $q$-Bernoulli polynomials associated with primitive Dirichlet character $χ$. Indeed, this function is the $q$-extension of two-variable $p$-adic $L$-function due to Fox, corresponding to the case $q=1 .$ Finally, we give some $p$-adic integral representation for this two-variable $p$-adic $q$-$L$-function and derive to $q$-extension of the generalized formula of Diamond and Ferro and Greenberg for the two-variable $p$-adic $L$-function in terms of the $p$-adic gamma and $\log$ gamma function.
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A New approach to q-zeta function
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
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Sums of powers of consecutive q-integers
We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.
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