### 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 language | English |
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Title of host publication | Proceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 |

Editors | Ratna Yuniati, Terry Mart, Ivandini T. Anggraningrum, Djoko Triyono, Kiki A. Sugeng |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735417410 |

DOIs | |

Publication status | Published - 22 Oct 2018 |

Event | 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 - Bali, Indonesia Duration: 26 Jul 2017 → 27 Jul 2017 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2023 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 |
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Country | Indonesia |

City | Bali |

Period | 26/07/17 → 27/07/17 |

### Keywords

- Chebyshev polynomials
- Composita
- composition of generating function
- generating function

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## Cite this

*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