Ein p-adisches Integral und seine Anwendungen II

Abstract

In part 1 [12] there is defined an integral on open and compact subsets of the rational p-adic field$\not Q_p$ with values in an algebraically closed and complete extension of$\not Q_p$. In this part we will compute so-called generalized p-Bernoulli numbers defined by

$$\int\limits_{|u| = 1} { u^k du for k \in \mathbb{Z}}$$

and prove their properties, which are important for the integration of Laurent-series. Furthermore we study several p-adic functions defined by the integral.