Fungrim entry: 166402

\lambda(\tau) = \frac{\wp\!\left(\frac{1}{2} \left(1 + \tau\right), \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}{\wp\!\left(\frac{1}{2}, \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\lambda(\tau) = \frac{\wp\!\left(\frac{1}{2} \left(1 + \tau\right), \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}{\wp\!\left(\frac{1}{2}, \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`WeierstrassP`	$\wp\!\left(z, \tau\right)$	Weierstrass elliptic function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("166402"),
    Formula(Equal(ModularLambda(tau), Div(Sub(WeierstrassP(Mul(Div(1, 2), Add(1, tau)), tau), WeierstrassP(Div(tau, 2), tau)), Sub(WeierstrassP(Div(1, 2), tau), WeierstrassP(Div(tau, 2), tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Modular lambda function