A normal form and integration in finite terms for a class of elementary functions

Hernan Cendra

Vol. 121 (1986), No. 1, 51–66

DOI: 10.2140/pjm.1986.121.51

Abstract

Let C be the field of complex numbers, E the usual exponential on C. So (C,E) is an exponential field.

We define an exponential ring extension C{x}^E of (C,E) and give a functional representation: C{x}^E is isomorphic to the smallest exponential ring extension of (C,E) containing the functions x^s, x a real and positive variable, and s ∈ C.

Finally, we give a simple integration-in-finite-terms algorithm for elements of C{x}^E.

Mathematical Subject Classification 2000

Primary: 12H05

Milestones

Received: 21 July 1982

Revised: 4 April 1985

Published: 1 January 1986