IJPAM: Volume 45, No. 2 (2008)

A GENERALIZATION OF D.W. BRESTER'S FORMULAE

Manuel A. Aguirre

, Emilo A. Aguirre Rébora

$^{1,2}$ Núcleo Consolidado Matemática Pura y Aplicada
Departamento de Matemática
Facultad de Ciencias Exactas
Universidad Nacional del Centro
Tandil, ARGENTINA

e-mail: maguirre@exa.unicen.edu.ar

e-mail: emrebora@exa.unicen.edu.ar

Abstract.Let be $\ G=G(x,m)$ defined by $\left( {\displaystyle\sum\limits_{i=1}^{\mu}} x_{i}^{2}\right) ^{m}-\left( {\displaystyle\sum\limits_{i=\mu+1}^{\mu+\nu}} x_{i}^{2}\right) ^{m}$ , where is integer postive and $\mu+\nu=n$ dimension of the space. In this paper we give a sense to residue of $(c^{2}% +G)_{+}^{\lambda}$ and $(c^{2}+G)_{-}^{\lambda}$ at $\lambda=-k$ , , where $(c^{2}+G)_{+}^{\lambda}$ is defined by () and $(c^{2}+G)_{-}^{\lambda}$ by (). Our formulae are generalization of the formulae () and () due to D.W. Bresters [#!B!#].