Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonicfunction, then so is V (r, θ) = U(1/r, −θ).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 10E
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Let (r, θ) denote the usual polar coordinates. Show that if U(r, θ) is a harmonic
function, then so is V (r, θ) = U(1/r, −θ).

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