The algebra of holonomic equations

Summary. In this article algorithmic methods are presented that have essentially been introduced into computer algebra systems like Maple, Mathematica or REDUCE within the last decade. The main ideas are due to Stanley and Zeilberger. Some of them had already been discovered in the last century by Beke, but because of their complexity the underlying algorithms have fallen into oblivion. We give a survey of these techniques, show how they can be used to identify transcendental functions, and present implementations of these algorithms in computer algebra systems. Received: 21.2.1996 / Accepted: 22.1.1997     

Properties of the vacuum. 2. Electrodynamic

The behaviour of a charged scalar field in an external electric field is discussed. Vacuum polarization is calculated by explicit summation of modes. Instabilities encountered in the external field approximation are absent when back reaction effects are included through a self-consistent semiclassical procedure.