The Weierstrass elliptic function is a fundamental object in the theory of elliptic functions, which are special functions that have a periodic nature in two directions. These functions are used extensively in various fields of mathematics, including complex analysis, algebraic geometry, and number theory.
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For a period lattice , the Weierstrass elliptic function is the normally convergent lattice sumIt is an even elliptic function with a double pole of principal part and zero residue at every point of the period lattice.