Bergman kernel K_D(z,w̄) = 1/(π(1-zw̄)²); K_D(0,0̄) = 1/π

The Bergman reproducing kernel of the open unit disk D = {|z| < 1} on the Hilbert space A²(D) = L²(D) ∩ Hol(D) is K_D(z, w̄) = 1/(π(1 − zw̄)²) — the unique holomorphic-in-z, antiholomorphic-in-w kernel with reproducing property ⟨f, K_D(·,…