R 3 , even with respect to each variable, therefore de?ne analytic functions of (x 2 ; y 2 ; z 2 ) Thus A (kXk ; kY k ; kX + Y k) is an analytic function of (X; Y ) 2 p p and the same holds for B. Since jx yj z x + y for the chosen values we have 0 B(x; y; z) < 1=2, which implies analyticity of the hypergeometric factor too. The theorem now follows from Proposition 3, p.23 ,
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