Some Identities and a Matrix Inverse Related to the Chebyshev Polynomials of the Second Kind and the Catalan Numbers
نویسندگان
چکیده
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, derive the inverse of an integer, unit, and lower triangular matrix, acquire a binomial inversion formula, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials of the second kind, the central Delannoy numbers, and the Fibonacci polynomials. E-mail addresses: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]. 2010 Mathematics Subject Classification. Primary 11B83; Secondary 05A15, 05A19, 11C08, 11C20, 11Y35, 15A09, 15B36, 33C05, 34A34.
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