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..