(Taylor decomposition in Peano
form) If a function
is
times differentiable at
then
Proposition
(Taylor decomposition in Schlomilch, Lagrange and Cauchy forms) If
a function
is
times differentiable in
,
then
where
admits any of the following representations:
(a)
(b)
(c)
for
and
.
Proposition
(Integral form of Taylor
decomposition) If a function
has
derivatives in finite interval between
and
,
and
is in
in such interval
then
