ABSTRACT

Technical Report Number: CS-96-21

Title:	Length of Finite Pierce Series:
	Theoretical Analysis and Numerical Computations

Author:			 Vlado Keselj
			 vkeselj@barrow.uwaterloo.ca

Institution:		 University of Waterloo

Abstract:
  Any real number  x  from the interval  (0,1]  can be represented as
  a unique Pierce series

     1      1        1
    --- - ----- + -------- - ...
     q1   q1*q2   q1*q2*q3

  where  {q1, q2, q3, ...}  is an increasing sequence of positive
  integers. The series is finite if and only if the number  x  is
  rational. This paper discusses the length of the series and the
  final results are a new upper bound (Theorem 2) and a new lower
  bound (Theorem 3) on the length.

  The numerical computations concerning the length are done by
  computer and the algorithms used and results are presented. The
  numerical results are an extension to the tables previously
  published.