be a sequence of functions, all defined on the same domain
This sequence converges pointwise towards a function
, defined on
if, for any
, the sequence
depends not only on
, but on the point
be a sequence of functions. The series of functionsConsider the sequence of functions
defined on the interval [0,1] by
, the following holds:
, the sum of the series is given by
and at 1, the series is divergent (sum of a series with a non zero constant general term).
is pointwise convergent if the sequence of partial
is pointwise convergent.