• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.331-343
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• 2023

In this paper, we give explicit identities for the degenerate q-poly-tangent numbers and polynomials. Finally, we obtain the relation of degenerate q-poly-tangent polynomials and Stirling numbers of the first kind and Stirling numbers of the second kind.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.133-144
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• 2020

In this paper, we discuss generalized q-poly-Euler numbers and polynomials. To do so, we define generalized q-poly-Euler polynomials with variable a and investigate its identities. We also represent generalized q-poly-Euler polynomials E^(k)_n,q(x; a) using Stirling numbers of the second kind. So we explore the relation between generalized q-poly-Euler polynomials and Stirling numbers of the second kind through it. At the end, we provide symmetric properties related to generalized q-poly-Euler polynomials using alternating power sum.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.29-38
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• 2018

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.781-798
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• 2019

This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.475-489
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• 2018

In this paper, by using the polylogarithm function, we introduce a generalized poly-Bernoulli numbers and polynomials with variable a. We find several combinatorial identities and properties of the polynomials. We give some properties that is connected with the Stirling numbers of second kind. Symmetric properties can be proved by new configured special functions. We display the zeros of the generalized poly-Bernoulli polynomials with variable a and investigate their structure.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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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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• v.41 no.4
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.197-209
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• 2023

In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.

• 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.