Deriving the explicit formula of Chebyshev polynomials of the third kind and the fourth kind

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Abstract

In this paper, we derived the explicit formula of Chebyshev polynomials of the third kind and the fourth kind by using a composita FΔ(n,k) of a generating function F(t)=σn>0fntn. By multiplying (1 - t) to the composition of generating function, G(t)=11-tandF(x,t)=2xt-t2, that has a composita FΔ(n,k), the coefficients of chebysshev polynomials of the third kind can be found. Moreover, by multiplying (1 + t) to the composition of generating functions G(t)=11-tandF(x,t)=2xt-t2, that has a composita FΔ(n,k), the coefficients of chebyshev polynomials of the fourth kind can be obtained. From those coefficients, the explicit formula of chebyshev polynomials of the third and the fourth kinds are derived.

Original languageEnglish
Title of host publicationProceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
EditorsRatna Yuniati, Terry Mart, Ivandini T. Anggraningrum, Djoko Triyono, Kiki A. Sugeng
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735417410
DOIs
Publication statusPublished - 22 Oct 2018
Event3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 - Bali, Indonesia
Duration: 26 Jul 201727 Jul 2017

Publication series

NameAIP Conference Proceedings
Volume2023
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
CountryIndonesia
CityBali
Period26/07/1727/07/17

Keywords

  • Chebyshev polynomials
  • Composita
  • composition of generating function
  • generating function

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    Dewi, I. P., Utama, S., & Aminah, S. (2018). Deriving the explicit formula of Chebyshev polynomials of the third kind and the fourth kind. In R. Yuniati, T. Mart, I. T. Anggraningrum, D. Triyono, & K. A. Sugeng (Eds.), Proceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 [020202] (AIP Conference Proceedings; Vol. 2023). American Institute of Physics Inc.. https://doi.org/10.1063/1.5064199