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Fungrim entry: de9f42

σ ⁣(z+τ,τ)=exp ⁣(2(z+τ2)ζ ⁣(τ2,τ))σ ⁣(z,τ)\sigma\!\left(z + \tau, \tau\right) = -\exp\!\left(2 \left(z + \frac{\tau}{2}\right) \zeta\!\left(\frac{\tau}{2}, \tau\right)\right) \sigma\!\left(z, \tau\right)
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\sigma\!\left(z + \tau, \tau\right) = -\exp\!\left(2 \left(z + \frac{\tau}{2}\right) \zeta\!\left(\frac{\tau}{2}, \tau\right)\right) \sigma\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
WeierstrassSigmaσ ⁣(z,τ)\sigma\!\left(z, \tau\right) Weierstrass sigma function
Expez{e}^{z} Exponential function
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("de9f42"),
    Formula(Equal(WeierstrassSigma(Add(z, tau), tau), Neg(Mul(Exp(Mul(Mul(2, Add(z, Div(tau, 2))), WeierstrassZeta(Div(tau, 2), tau))), WeierstrassSigma(z, tau))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 11:00:55.020619 UTC