• Journal of applied mathematics & informatics
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• v.31 no.5_6
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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 mathematics & informatics
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• v.30 no.1_2
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• pp.321-325
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• 2012

In this paper, we consider twisted $q$-Euler polynomials and define a $p$-adic $q$-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the $p$-adic $q$-transfer operator on the space of twisted $q$-Euler polynomials.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.553-563
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• 2013

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.375-387
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• 2023

In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.125-132
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• 2006

It is the aim of this paper to introduce the Genocchi numbers Gn and polynomials Gn(x) and to display the shape of Genocchi polynomials Gn(x). Finally, we investigate the roots of the Genocchi polynomials Gn(x).

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.37-56
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• 2020

In this paper we discuss some interesting properties of (p, q)-special polynomials and derive various relations. We gain some relations between (p, q)-zeta function and (p, q)-special polynomials by considering (p, q)-analogue Euler sum types. In addition, we derive the relationship between (p, q)-polylogarithm function and (p, q)-special polynomials.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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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.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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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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• v.39 no.3_4
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• pp.405-417
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• 2021

The aim of this paper is to provide the residues of Euler polynomials modulo p² in terms of alternating sums of like powers of numbers in arithmetical progression. Also, we establish the analogue of a classical congruence of Lehmer.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1003-1019
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• 2022

In this paper, by using the multiple fermionic p-adic integrals, we obtain Kummer-type congruences for the higher order Euler numbers and polynomials.