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Q65Section II (Mathematics)65 of 190

A mean-value computation whose printed option is ambiguously typeset

Let u(r,θ)u(r,\theta) be a harmonic function in the disc D={(r,θ)/0≤r<R,−π<θ≤π}D=\{(r,\theta)/0\le r<R,-\pi<\theta\le\pi\} such that uu is continuous in closed disc Dˉ\bar D and satisfies: u(R,θ)=cos⁡θ,∣θ∣≤π/3u(R,\theta)=\cos\theta, |\theta|\le\pi/3, =0, π/3<∣θ∣≤π=0,\ \pi/3<|\theta|\le\pi. The mean value theorem gives the value of u(0,0)u(0,0) as:

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