Abstract
In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials of the second kind, conclude the inverse of an integer, unit, and lower triangular matrix, derive an inversion theorem, present sev-eral identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers with the Chebyshev polynomials of the second kind, the central Delannoy numbers, and the Fibonacci polynomials respectively.
Original language | English (US) |
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Pages (from-to) | 518-541 |
Number of pages | 24 |
Journal | Applicable Analysis and Discrete Mathematics |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Keywords
- Bell polynomial of the second kind
- Binomial inversion formula
- Catalan number
- Chebyshev polynomials of the second kind
- Classical hypergeometric function
- Explicit formula
- Generating function
- Identity
- Integral representation
- Inverse matrix
- Triangular matrix
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics