Second-order Hadamard lemma
= Second-order Hadamard lemma
{c}
For a <smooth function> $f(x,y)$,
$$
f(x,y)=f(x,0)+yD_2f(x,0)+y^2h(x,y),
$$
where the smooth remainder is
$$
h(x,y)=\int_0^1(1-t)D_2^2f(x,ty)\,dt.
$$
= Second-order Hadamard lemma
{c}
For a <smooth function> $f(x,y)$,
$$
f(x,y)=f(x,0)+yD_2f(x,0)+y^2h(x,y),
$$
where the smooth remainder is
$$
h(x,y)=\int_0^1(1-t)D_2^2f(x,ty)\,dt.
$$