• 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.40 no.1_2
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• pp.371-391
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• 2022

In this paper we give some prperties of the poly-cosine tangent polynomials and poly-sine tangent polynomials.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.123-139
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• 2022

In this paper we give some interesting properties of the cosine tangent polynomials and sine tangent polynomials. In addition, we give some identities for these polynomials and the distribution of zeros of these polynomials.

• 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.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.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.6
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• pp.1365-1376
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• 2023

In this paper, we construct higher-order poly-tangent polynomials and study several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order poly-tangent polynomials.

• 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 the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.487-494
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• 2016

In this paper, we study differential equations arising from the generating functions of tangent numbers. We give explicit identities for the tangent numbers.