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The second generalized GK maximal curves GK_2,n are maximal curves over finite fields with q^2n elements, where q is a prime power and n ≥ 3 an odd integer, constructed by Beelen and Montanucci. In this paper we determine the structure of the Weierstrass semigroup H(P) where P is an arbitrary F_q^2-rational point of GK_2,n. We show that these points are Weierstrass points and the Frobenius dimension of GK_2,n is computed. A new proof of the fact that the first and the second generalized GKarXiv:1901.08897v1 fatcat:r5hphb4r5jgzlfn3xbbaczywcy