and
can be used in the following way.
University Maths Notes: Complex Analysis – Using Cauchy's Integral Formula
Cauchy's integral formula statesand
can be used in the following way.
Evaluate
where
is
the circle
is
entire and
is
in the interior ofhence
Evaluate
where
is
the circle
which
in the interior of
is
entire hence
Evaluate
where
is
the circle
has
roots
both
insideso
we write
and
separate the integrand into partial fractions, obtaining
sin z is entire hence
Evaluate
where
is
the circle
lie
insidebut
-2 is outside. We rewrite the integrand using partial fractions.
