Exact sympy verification of the mean-value property on the harmonic polynomial u(x, y) = x² − y² (the real part of z² = (x+iy)²). Step 1 — Laplacian: ∂²u/∂x² = 2, ∂²u/∂y² = −2, so Δu = 0 identically. Step 2 — mean value over the circle…
Exact sympy verification of the mean-value property on the harmonic polynomial u(x, y) = x² − y² (the real part of z² = (x+iy)²). Step 1 — Laplacian: ∂²u/∂x² = 2, ∂²u/∂y² = −2, so Δu = 0 identically. Step 2 — mean value over the circle…