• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.643-654
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• 2021

In this paper, we define a modified q-poly-Bernoulli polynomials of the first type and modified q-poly-tangent 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.

• Journal of applied mathematics & informatics
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• 제38권3_4호
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• pp.301-309
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• 2020

Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.

• 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.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.145-157
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• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.623-630
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• 2013

In this paper, our aim is finding the term of generalized Eule polynomials. We also obtain some identities and relations involving the Bernoulli numbers, the Euler numbers and the Stirling numbers.

• 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.

• 호남수학학술지
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• 제39권2호
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• pp.217-231
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• 2017

In this paper, we introduce a generating function for a Legendre-based poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. By making use of the generating function method and some functional equations mentioned in the paper, we conduct a further investigation in order to obtain some implicit summation formulae for the Legendre-based poly-Bernoulli numbers and polynomials.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.