A new family of periodic functions as explicit roots of a class of polynomial equations

Marc Artzrouni (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

For any positive integer n, a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equation of order n. The n roots are the values of the appropriate function from that family taken at 0,1,...,n-1.

Mots clés: polynomial equation; power series; Catalan numbers; discrete convolution

Domaines: Mathématiques générales [math.GM]

Marc Artzrouni. A new family of periodic functions as explicit roots of a class of polynomial equations. Australian Journal of Mathematical Analysis and Applications, 2006, 3 (2), pp.4; 1-16. ⟨hal-00003146⟩