Solution
= Solution
For $f(x)=1/(x^2+1)$, contour integration or partial fractions gives
$$
Hf(y)=\frac{y}{1+y^2}
$$
under the convention in part (b). Therefore
$$
\boxed{Hf(-1)=-\frac12}.
$$
= Solution
For $f(x)=1/(x^2+1)$, contour integration or partial fractions gives
$$
Hf(y)=\frac{y}{1+y^2}
$$
under the convention in part (b). Therefore
$$
\boxed{Hf(-1)=-\frac12}.
$$