Identities involving Narayana polynomials and Catalan numbers

Toufik Mansour, Yidong Sun

Research output: Contribution to journalArticlepeer-review


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. Crown

Original languageEnglish
Pages (from-to)4079-4088
Number of pages10
JournalDiscrete Mathematics
Issue number12
StatePublished - 28 Jun 2009

Bibliographical note

Funding Information:
The authors are grateful to the anonymous referees for the helpful suggestions and comments. The second author was supported by The National Science Foundation of China (10801020).


  • Catalan numbers
  • Inverse relations
  • Legendre polynomials
  • Narayana polynomials

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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