TY - GEN

T1 - Deriving the explicit formula of Chebyshev polynomials of the third kind and the fourth kind

AU - Dewi, I. P.

AU - Utama, S.

AU - Aminah, S.

N1 - Publisher Copyright:
© 2018 Author(s).

PY - 2018/10/22

Y1 - 2018/10/22

N2 - 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.

AB - 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.

KW - Chebyshev polynomials

KW - Composita

KW - composition of generating function

KW - generating function

UR - http://www.scopus.com/inward/record.url?scp=85056107346&partnerID=8YFLogxK

U2 - 10.1063/1.5064199

DO - 10.1063/1.5064199

M3 - Conference contribution

AN - SCOPUS:85056107346

T3 - AIP Conference Proceedings

BT - Proceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017

A2 - Yuniati, Ratna

A2 - Mart, Terry

A2 - Anggraningrum, Ivandini T.

A2 - Triyono, Djoko

A2 - Sugeng, Kiki A.

PB - American Institute of Physics Inc.

T2 - 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017

Y2 - 26 July 2017 through 27 July 2017

ER -