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Fungrim entry: 151e42

ζ ⁣(z,τ) is holomorphic on zCΛ(1,τ)\zeta\!\left(z, \tau\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \Lambda_{(1, \tau)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\zeta\!\left(z, \tau\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \Lambda_{(1, \tau)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
CCC\mathbb{C} Complex numbers
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("151e42"),
    Formula(IsHolomorphic(WeierstrassZeta(z, tau), ForElement(z, SetMinus(CC, Lattice(1, tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-11-19 15:10:20.037976 UTC