1. Let be an arbitrary power series, and set
.
Then:
a) for , the series is everywhere convergent.
b) for , the series is divergent for every
.
c) if , then the series is absolutely convergent for every
with
, divergent for every
with
.
Thus in all three cases, with suitable interpretation:
references
Konrad Knopp – Infinite sequences and series, 1956