Weierstrass's Elliptic Functions
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High Quality Content by WIKIPEDIA articles! The Weierstrass elliptic function can be defined in three closely related ways, each of which possesses certain advantages. One is as a function of a complex variable z and a lattice in the complex plane. Another is in terms of z and two complex numbers 1 and 2 defining a pair of generators, or periods, for the lattice. The third is in terms z and of a modulus in the upper half-plane. This is related to the previous definition by = 2 / 1, which by the conventional choice on the pair of periods is in the upper half-plane. Using this approach, for fixe...
High Quality Content by WIKIPEDIA articles! The Weierstrass elliptic function can be defined in three closely related ways, each of which possesses certain advantages. One is as a function of a complex variable z and a lattice in the complex plane. Another is in terms of z and two complex numbers 1 and 2 defining a pair of generators, or periods, for the lattice. The third is in terms z and of a modulus in the upper half-plane. This is related to the previous definition by = 2 / 1, which by the conventional choice on the pair of periods is in the upper half-plane. Using this approach, for fixed z the Weierstrass functions become modular functions of .
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