Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials

Kang, Jung Yoog; Ryoo, Chen Seoung

doi:10.3390/math8040463

Open AccessFeature PaperArticle

Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials

by

Jung Yoog Kang

^1,* and

Chen Seoung Ryoo

²

¹

Department of Mathematics Education, Silla University, Busan 46958, Korea

²

Department of Mathematics, Hanman University, Daejeon 34430, Korea

^*

Author to whom correspondence should be addressed.

Mathematics 2020, 8(4), 463; https://doi.org/10.3390/math8040463

Submission received: 20 February 2020 / Revised: 17 March 2020 / Accepted: 20 March 2020 / Published: 25 March 2020

(This article belongs to the Special Issue Special Functions and Applications)

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Abstract

In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots. Through numerical experimentation, we look for various assumptions about the polynomials above.

Keywords: q-cosine Bernoulli polynomials; q-sine Bernoulli polynomials; q-numbers; q-trigonometric function

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MDPI and ACS Style

Kang, J.Y.; Ryoo, C.S. Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials. Mathematics 2020, 8, 463. https://doi.org/10.3390/math8040463

AMA Style

Kang JY, Ryoo CS. Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials. Mathematics. 2020; 8(4):463. https://doi.org/10.3390/math8040463

Chicago/Turabian Style

Kang, Jung Yoog, and Chen Seoung Ryoo. 2020. "Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials" Mathematics 8, no. 4: 463. https://doi.org/10.3390/math8040463

APA Style

Kang, J. Y., & Ryoo, C. S. (2020). Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials. Mathematics, 8(4), 463. https://doi.org/10.3390/math8040463

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials

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