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Some identities involving Chebyshev polynomials, Fibonacci polynomials and their derivatives

Some identities involving Chebyshev polynomials, Fibonacci polynomials and their derivatives

In this paper, we will derive the explicit formulae for Chebyshev polynomials of the third and fourth kind with odd and even indices using the combinatorial method. Similar results are also deduced for their r-th derivatives. Finally, some identities involving Chebyshev polynomials of the third and fourth kind with even …