Yes.
Let , let , and get
Let .
which is holomorphic on , hence after , for
That is the principlal part of at , and so is the principle part, after , of at infinity.
Thus is the principle part of at infinity.
Yes.
Let , let , and get
Let .
which is holomorphic on , hence after , for
That is the principlal part of at , and so is the principle part, after , of at infinity.
Thus is the principle part of at infinity.