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Symmetric Properties of the Generalized Tangent Polynomials and Computation of their Zeros

Journal of Knowledge Information Technology and Systems
Abbr : JKITS
2019, 14(2), pp.171-181
DOI : 10.34163/jkits.2019.14.2.007
Publisher : Korea Knowledge Information Technology Society
Research Area : Interdisciplinary Research

1고려대학교
2고려대학교
3고려대학교 • ABSTRACT

This study describes the symmetrical properties and root calculations of generalized tangent polynomials following the study of the generalized tangent polynomials using the characteristics of numbers. The generalized tangent polynomial has the relational characteristics of the number of Genocchi and the polynomial of Genocchi, and the number of Euler and the polynomial of Euler. In this study, the symmetrical properties of generalized tangent polynomials are demonstrated by dividing them into three parts. This study also uses the Mathematica software program to approach numerically. The results of symmetrical properties are identified by graphs and figures through the Mathematica software program. Next, the calculation of root for generalized tangent polynomials is taken, for example, when the generalized tangent polynomial index is 3. The calculation of root of generalized tangent polynomial is shown by tables and graphs through the Mathematica software program. In this study, the symmetrical properties and root calculations of generalized tangent polynomials were conducted through the Mathematica software program. As a result, two guesses were possible in this study. The first generalized tangent polynomial would be a function of reflective substitution analytical plurality, and the second generalized tangent polynomial would have real zeros. Looking forward to a numerical approach using the Mathematica software program in the field of generalized tangent polynomial research, this study concludes.
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