## Annals of Mathematics |

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Ai(x An(x analytic function angle arbitrary asymptote coefficients condition consider constant contains continuous convergent series coordinates corresponding coupure defined definition denote derived determined df/dp dg/dp differential equation domaine envelope exists expression finite number follows formula functional equation Gamma function given gives Hence holomorphic hypersurfaces identity infinite infinity intersection interval iteration J. W. ALEXANDER linear lines of curvature maps the interior Math matrix monotone negative neighborhood normal notation obtain one-valued origin parameter peut poles polynomial positive integer power series Princeton property Pol proved pseudospherical surface quadric radius real function real values region Rn relation respect satisfied self-projective curves simple region singular points solution star-shaped region subscripts sufficient suppose tangent theorem theta theta function tion Type uniformly convergent unit circle unity valeur vanish variables vers whence zero