P-adic analysis and the calculus of finite differences

L. Van Hamme
Vrije Universiteit Brussel
Faculteit Toegepaste Wetenschappen
Brussels, Belgium

Date:

Abstract:

It is well known that the role of the calculus of finite differences is much greater in p-adic analysis than in real or complex analysis. This paper confirms this once again. Our main result is a finite difference expansion for the derivative of an odd C¹ function. The formula is fairly general since it depends on an arbitrary bounded sequence.