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Fungrim entry: a95b7e

 ⁣(z+m+nτ,τ)= ⁣(z,τ)\wp\!\left(z + m + n \tau, \tau\right) = \wp\!\left(z, \tau\right)
Assumptions:zC  and  τH  and  zΛ(1,τ)  and  mZ  and  nZz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
\wp\!\left(z + m + n \tau, \tau\right) = \wp\!\left(z, \tau\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
WeierstrassP ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("a95b7e"),
    Formula(Equal(WeierstrassP(Add(Add(z, m), Mul(n, tau)), tau), WeierstrassP(z, tau))),
    Variables(z, tau, m, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)), Element(m, ZZ), Element(n, ZZ))))

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2021-03-15 19:12:00.328586 UTC