AbstractWe 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
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
AbstractWe show that Narayana polynomials are a specialization of row Hall–Littlewood symmetric func...
25 pages, LaTeX, to appear in Advances in Applied MathematicsInternational audienceWe show that Nara...
25 pages, LaTeX, to appear in Advances in Applied MathematicsInternational audienceWe show that Nara...
AbstractBased on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find...
AbstractWe first establish the result that the Narayana polynomials can be represented as the integr...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
In the paper, the authors collect several integral representations of the Catalan numbers and centra...
In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi ...
Abstract. Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we fi...
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence,...
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
AbstractWe show that Narayana polynomials are a specialization of row Hall–Littlewood symmetric func...
25 pages, LaTeX, to appear in Advances in Applied MathematicsInternational audienceWe show that Nara...
25 pages, LaTeX, to appear in Advances in Applied MathematicsInternational audienceWe show that Nara...
AbstractBased on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find...
AbstractWe first establish the result that the Narayana polynomials can be represented as the integr...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
The Narayana identity is a well-known formula that expresses the classical Catalan numbers as sums o...
In the paper, the authors collect several integral representations of the Catalan numbers and centra...
In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi ...
Abstract. Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we fi...
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence,...
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternativ...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
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