A method of summing infinite series

Abstract

This paper describes a new method of obtaini ng an equivalent series from a given infi ni te co nv ergent or diverge nt series. I n many cases the new series is more convenient for su mming t.han the original and, moreover, the same method may usually be repeated indefinitely to obtain an entire sequence of series each equivalent t o t he original and each better than its predecessor in s umming propert ies. 'lh e new method differs from most s umming methods heretofore employed in that terms of t he transformed series are not linear function s of terms of the origin al series. The paper includes proofs of theor ems indicating the s cope of the new m ethod and comparisons of results with various other m ethods for many specific examples.