An Interpolation Series for Continuous Functions of a p-adic Variable.

The theory of analytic functions of a p-adic variable (i. e. of functions defined by power series) is much simpler than that of complex analytic funktions and offers few surprises. On the other band, the behaviour of continuous functions of a p-adic variable is quite distinct from that of real continuous functions, and many basic theorems of real analysis have no p-adic analogues. Thus there is no simple analogue to the mean value ix\ theorem of differential calculus, even for polynomials like l l ; there exist infinitely many