• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.165-186
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• 2023

In this paper we give some prperties of the (p, q)-poly-cosine tangent polynomials and (p, q)-poly-sine tangent polynomials.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.205-212
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• 2018

In this paper, we study linear differential equations arising from the generating functions of twisted (h, q)-tangent polynomials. We give explicit identities for the twisted (h, q)-tangent polynomials.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.83-91
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• 2021

In this paper, we introduce the concepts of q-cosine tangent polynomials and q-sine tangent polynomials. From these polynomials, we find some identities and properties by using q-numbers and q-trigonometric functions.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.115-120
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• 2018

In this paper, we discover symmetric properties for generalized Carlitz's q-tangent polynomials.

• 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.42 no.2
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• pp.457-469
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• 2024

In this paper, we construct higher-order (p, q)-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order (p, q)-poly-tangent polynomials.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.495-504
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• 2017

In this paper we construct the Carlitz's type q-tangent numbers $T_{n,q}$ and polynomials $T_{n,q}(x)$. From these numbers and polynomials, we establish some interesting identities and relations.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.291-301
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• 2023

In this paper, we investigate the zeros of the fully modified q-poly-tangent polynomials of the first type.

• 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 mathematics & informatics
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• v.35 no.1_2
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• pp.113-120
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• 2017

In this paper, we introduce degenerate tangent numbers ${\mathcal{T}}^{(k)}_{n,q}({\lambda})$ and tangent polynomials ${\mathcal{T}}^{(k)}_{n,q}(x,{\lambda})$ of higher order. Finally, we obtain interesting properties of these numbers and polynomials.