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Fungrim entry: 1c25d3

η(τ)=i2πη(τ)ζ ⁣(12,τ)\eta'(\tau) = \frac{i}{2 \pi} \eta(\tau) \zeta\!\left(\frac{1}{2}, \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta'(\tau) = \frac{i}{2 \pi} \eta(\tau) \zeta\!\left(\frac{1}{2}, \tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
ConstIii Imaginary unit
Piπ\pi The constant pi (3.14...)
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("1c25d3"),
    Formula(Equal(ComplexDerivative(DedekindEta(tau), For(tau, tau)), Mul(Mul(Div(ConstI, Mul(2, Pi)), DedekindEta(tau)), WeierstrassZeta(Div(1, 2), tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-11-19 15:10:20.037976 UTC