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Fungrim entry: b96c9d

σ ⁣(z,τ)=exp ⁣(z26θ1 ⁣(0,τ)θ1 ⁣(0,τ))θ1 ⁣(z,τ)θ1 ⁣(0,τ)\sigma\!\left(z, \tau\right) = \exp\!\left(-\frac{{z}^{2}}{6} \frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)}\right) \frac{\theta_{1}\!\left(z , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\sigma\!\left(z, \tau\right) = \exp\!\left(-\frac{{z}^{2}}{6} \frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)}\right) \frac{\theta_{1}\!\left(z , \tau\right)}{\theta'_{1}\!\left(0 , \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
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("b96c9d"),
    Formula(Equal(WeierstrassSigma(z, tau), Mul(Exp(Mul(Neg(Div(Pow(z, 2), 6)), Div(JacobiTheta(1, 0, tau, 3), JacobiTheta(1, 0, tau, 1)))), Div(JacobiTheta(1, z, tau), JacobiTheta(1, 0, tau, 1))))),
    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.

2019-09-16 21:17:18.797188 UTC