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

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)=∑n>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...

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Bibliographic Details
Main Authors: Dewi, I. P., Utama, S., Aminah, S.
Format: Conference Proceeding
Language:English
Subjects:
Chebyshev approximation
Coefficients
Composition
Ice
Mathematical analysis
Poisson distribution
Polynomials
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Summary: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)=∑n>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.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5064199