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Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre's arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using ( p , k )-parametrization in terms of Borweins' theta functions.doi:10.1155/2021/6614572 fatcat:hkfpqd5wjnes7hza62o2mngwcq