The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)

A detailed and unified treatment of $P$-adic differential equations, from the basic principles to the current frontiers of research.

The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ̃ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to

Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of b