On Jensen's and related combinatorial identities | Zendy

Victor J. W. Guo | Zendy

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On Jensen's and related combinatorial identities

Author(s) -

Victor J. W. Guo

Publication year - 2011

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm110717017g

Subject(s) - mathematics , identity (music) , combinatorics , generalization , mathematical proof , combinatorial proof , simple (philosophy) , multinomial distribution , discrete mathematics , mathematical analysis , physics , geometry , statistics , philosophy , epistemology , acoustics

Motivated by the recent work of Chu [Electron. J. Combin. 17 (2010), #N24], we give simple proofs of Jensen's identity and Chu's and Mohanty-Handa's generalizations of Jensen's identity. We also give a simple proof of an equivalent form of Graham-Knuth-Patashnik's identity which was rediscovered, respectively, by Sun in 2003 and Munarini in 2005. Finally we give a multinomial coefficient generalization of this identity.

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