where g ( λ λ , θ θ ) = f ( λ λ − − π π , θ θ ) and h ( λ λ , θ θ ) = f ( λ λ , θ θ ) for ( λ λ , θ θ ) ∈ ∈ [ 0 , π π ] × × [ 0 , π π ] . The new function f ~ ~ is 2 π π -periodic in λ λ and θ θ , and is constant along the lines θ θ = 0 and θ θ = ± ± π π , corresponding to the poles.