PROGRESSIVE PATHS AND MULTINOMIALS IN r-DIMENSIONAL LATTICE TECNIQUE TO GENERALIZATION OF BINOMIAL IDENTITIES

Ruy Madsen BARBOSA[1]

§    ABSTRACT: The work gives new proofs of Tauber's summations, and of the second generalized form at the Vandermonde's convolution, with methodology of progressive paths. The main results are two new sucessives generalizations. The first is the generalization of a special property of binomial coefficients with alternate sums; and the second is, en advancement, the generalization of the third Tauber's summation and also of the simple summation of multinomial coefficients . Another mew result is a generalization to multinomial of the sum of multiplication of binomial coefficients by the order respective.

§    KEYWORDS: Progressive paths; higher dimensional lattice; multinomial coefficients; summations; generalizations; first and second form of Vandermonde's convolution.

 

 

 



[1]Professor aposentado - Instituto de Biociências , Letras e Ciências Exatas - UNESP - São José do Rio Preto - SP - Brasil. Professor Pesquisador das Faculdades Integradas Riopretense (FIRP) - 15025-400 - São José do Rio Preto - SP - Brasil..