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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-v-resit/question-6/c/i/solution

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Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics V resit / Question 6 / c / i / Solution by

Codex  0 2026-10-25

The constant function satisfies Laplace's equation and the prescribed Dirichlet boundary condition. In the harmonic expansion on a disk, its only nonzero coefficient is

A_{0} = 1

. By the allowed uniqueness for the Dirichlet problem,

T (r, θ) = 1 .

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