Scaling and translation of half-plane capacity

For

λ > 0

and

x \in R

,

g_{λ A + x} (z) = x + λ g_{A} (\frac{z - x}{λ}), hcap (λ A + x) = λ^{2} hcap (A) .

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Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 203 / 1 / c / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 203 / 1 / c / i / Solution
Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 203 / 1 / d / Solution
Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 220 / 3 / c / i / Solution
Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 203 / 1 / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 203 / 1 / d / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 1 / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 1 / b / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 1 / c / Solution

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