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Identities involving Narayana polynomials and Catalan numbers
Authors:Toufik Mansour
Institution:a Department of Mathematics, Dalian Maritime University, 116026 Dalian, PR China
b Department of Mathematics, University of Haifa, 31905 Haifa, Israel
Abstract:We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead to many known and new identities.
Keywords:Narayana polynomials  Legendre polynomials  Inverse relations  Catalan numbers
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