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Fungrim entry: 0e649f

ddzσ ⁣(z,τ)=ζ ⁣(z,τ)σ ⁣(z,τ)\frac{d}{d z}\, \sigma\!\left(z, \tau\right) = \zeta\!\left(z, \tau\right) \sigma\!\left(z, \tau\right)
Assumptions:zCandτHandzΛ(1,τ)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)}
TeX:
\frac{d}{d z}\, \sigma\!\left(z, \tau\right) = \zeta\!\left(z, \tau\right) \sigma\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)}
Definitions:
Fungrim symbol Notation Short description
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
WeierstrassSigmaσ ⁣(z,τ)\sigma\!\left(z, \tau\right) Weierstrass sigma function
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta 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
Source code for this entry:
Entry(ID("0e649f"),
    Formula(Equal(Derivative(WeierstrassSigma(z, tau), Tuple(z, z, 1)), Mul(WeierstrassZeta(z, tau), WeierstrassSigma(z, tau)))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)))))

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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