Weierstrass's Elliptic Functions
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High Quality Content by WIKIPEDIA articles! In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form (cf Jacobi's elliptic functions); they are named for Karl Weierstrass. This class of functions are also referred to as p-functions and generally written using the symbol (or wp) (a stylised letter p called Weierstrass p). 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…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form (cf Jacobi's elliptic functions); they are named for Karl Weierstrass. This class of functions are also referred to as p-functions and generally written using the symbol (or wp) (a stylised letter p called Weierstrass p). 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 .