Fungrim entry: b96c9d

\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:

z \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
`WeierstrassSigma`	$\sigma\!\left(z, \tau\right)$	Weierstrass sigma function
`Exp`	${e}^{z}$	Exponential function
`Pow`	${a}^{b}$	Power
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`CC`	$\mathbb{C}$	Complex numbers
`HH`	$\mathbb{H}$	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))))

Fungrim entry: b96c9d

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