Doubly infinite series is a series where ranges from to .
Doubly infinite series is a term which should be used with caution, as some people use the term for the double series (series with two indices), so that it is an infinite series in each variable, say .
Doubly infinite series
is a pair of two (ordinary infinite) series, its negative part and its positive part (one could say nonnegative part, but it is not customary). A doubly infinite series converges if each of its constituent parts (positive and negative), converges; the sum of the series is then, by definition, the sum of the limits of the two series.
Notion to cover later: principal value of a double series
finite set, finite series?, polynomial
integers, doubly infinite series, Laurent series
rational numbers, series indexed in rationals, Puiseux series
Last revised on May 9, 2021 at 03:24:37. See the history of this page for a list of all contributions to it.