The Green function G(x, y, z, t > 0) = (t r/c)/4r is a solution of

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The Green function G(x, y, z, t > 0) = δ(t − r/c)/4πr is a solution of the inhomogeneous wave equation in three space dimensions with the source term −δ(x)δ(y)δ(z)δ(t).
(a) Show that G2(x, y, t) = ∫∞ −∞ dz G(x, y, z, t) is a solution of the inhomogeneous wave equation in two space dimensions with the source term −δ(x)δ(y)δ(t).
(b) Evaluate the integral in part (a) to find G2(ρ, t) explicitly, where ρ= x+ y2.

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