Acceleration of convergence of series for certain multiple integrals

Abstract

Levin [1] has given a method for speeding up convergence of series. In this paper it is shown that Levin's method—and similar methods—do not work for certain types of series and an analysis is given to explain this phenomenon. It is also shown that Levin's method can be used to efficiently compute certain types of multiple integrals. A variation of a method of Van Wijngaarden is shown to be efficient in evaluating series of positive terms for which Levin's method does not work.

Keywords:

• Summation of series with positive terms
• Levin's method
• evaluation of integrals by series expansion
• Lattice Green functions

C.R. Categories:

• 5.12.
• 5.16