Conformal blocks obey the same conformal symmetry constraints as four-point functions. In particular, s-channel conformal blocks can be written in terms of functions g p ( s ) ( u , v ) of the cross-ratios. While the OPE O 1 ( x 1 ) O 2 ( x 2 ) only converges if | x 12 | < min ( | x 23 | , | x 24 | ) , conformal blocks can be analytically continued to all (non pairwise coinciding) values of the positions. In Euclidean space, conformal blocks are single-valued real-analytic functions of the positions except when the four points x i lie on a circle but in a singly-transposed cyclic order [1324], and only in these exceptional cases does the decomposition into conformal blocks not converge.