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The function
at its poles inside the unit circle around the origin.

The zeros of are the zeros of
the two equations

If the zeros of (1) are z₁ & z₂, the zeros of (2) are the
complex conjugates . If z₁ lies inside the unit
circle, so does . Therefore z₁ & are the only two [principle?]
poles inside the circle. Thus

The residue of f(z) at

The residue of f(z) at