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2015•Bulletin of Mathematical SciencesOpen access

A generalization of a combinatorial identity by Chang and Xu

Ulrich R. Abel, Vijay Gupta, Mircea Ivan

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Abstract

Recently, Chang and Xu gave a probabilistic proof of a combinatorial identity which involves binomial coefficients. Duarte and Guedes de Oliveira (J Integer Seq 16, 2013 ) extended the result. Applying a generalization of the Leibniz rule for higher derivatives of the product of functions yields a new short proof and a generalization of the above mentioned identity.

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Recently, Chang and Xu gave a probabilistic proof of a combinatorial identity which involves binomial coefficients. Duarte and Guedes de Oliveira (J Integer Seq 16, 2013 ) extended the result. Applying a generalization of the Leibniz rule for higher derivatives of the product of functions yields a new short proof and a generalization of the above mentioned identity.

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Available abstract

Recently, Chang and Xu gave a probabilistic proof of a combinatorial identity which involves binomial coefficients. Duarte and Guedes de Oliveira (J Integer Seq 16, 2013 ) extended the result. Applying a generalization of the Leibniz rule for higher derivatives of the product of functions yields a new short proof and a generalization of the above mentioned identity.

Key concepts: Generalization, Identity (music), Binomial coefficient, Combinatorial proof, Mathematics, Binomial (polynomial), Probabilistic logic, Product (mathematics)

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