Schwarz Integral Formula - Unit Disc

Unit Disc

Let ƒ = u + iv be a function which is holomorphic on the closed unit disc {z ∈ C | |z| ≤ 1}. Then

f(z) = \frac{1}{2\pi i} \oint_{|\zeta| = 1} \frac{\zeta + z}{\zeta - z} \text{Re}(f(\zeta)) \, \frac{d\zeta}{\zeta} + i\text{Im}(f(0))

for all |z| < 1.

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