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 -