• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.45-56
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• 2021

D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.

• 대한수학회지
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• 제55권5호
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• pp.1179-1192
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• 2018

Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.1-11
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• 2024

In this paper, we define a new fully modified q-poly-Euler numbers and polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

• 대한수학회보
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• 제42권3호
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• pp.491-499
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• 2005

Recently, Kim[2,6] has introduced an interesting Euler­Barnes' numbers and polynomials. In this paper, we construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their properties.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• 대한수학회지
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• 제37권1호
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• pp.21-30
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• 2000

We give a proof of the distribution relation for q-Bernoulli polynomials $B_{k}$(x : q) by using q-integral and evaluate the values of p-adic q-L-function.n.

• 호남수학학술지
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• 제33권4호
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• pp.529-534
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• 2011

In this paper, we consider the q-analogues of Euler numbers and polynomials using the fermionic p-adic invariant integral on $\mathbb{Z}_p$. From these numbers and polynomials, we derive some interesting identities and properties on the q-analogues of Euler numbers and polynomials.

• 대한수학회보
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• 제58권2호
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• pp.315-326
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• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.219-234
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• 2019

We use the definition of Euler polynomials of the second kind with (p, q)-numbers to identify some identities and properties of these polynomials. We also investigate some relationships between (p, q)-Euler polynomials of the second kind, (p, q)-Bernoulli polynomials, and (p, q)-tangent polynomials by using the properties of (p, q)-exponential function.

• 호남수학학술지
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• 제34권1호
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• pp.1-9
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• 2012

The purpose of this paper is to give a new construction of the extended q-Euler numbers and polynomials of higher-order with weight by using p-adic q-integral on $\mathbb{Z}_p$.