stylistic:style_transfer, quality:correction, structural:scholar_edition
Residue at infinity

In general, the residue at infinity is defined as:

If the following condition is met:

then the residue at infinity can be computed using the following formula:

If instead

then the residue at infinity is

For functions meromorphic on the entire complex plane with finitely many singularities, the sum of the residues at the (necessarily) isolated singularities plus the residue at infinity is zero, which gives: