Sympy-verified symbolic integral pin: for r = 1/2 the normalisation identity (1/(2π)) ∫_0^{2π} P_r(θ) dθ = 1 for the unit-disk Poisson kernel P_r(θ) = (1 − r²)/(1 − 2r cos θ + r²). Evaluation: substitute r = 1/2 to get P(θ) = (3/4)/(5/4 −…
Sympy-verified symbolic integral pin: for r = 1/2 the normalisation identity (1/(2π)) ∫_0^{2π} P_r(θ) dθ = 1 for the unit-disk Poisson kernel P_r(θ) = (1 − r²)/(1 − 2r cos θ + r²). Evaluation: substitute r = 1/2 to get P(θ) = (3/4)/(5/4 −…