Fungrim entry: 124339

\wp\!\left(f(z), \tau\right) = z\; \text{ where } f(z) = R_F\!\left(z - e_{1}\!\left(\tau\right), z - e_{2}\!\left(\tau\right), z - e_{3}\!\left(\tau\right)\right)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

TeX:

\wp\!\left(f(z), \tau\right) = z\; \text{ where } f(z) = R_F\!\left(z - e_{1}\!\left(\tau\right), z - e_{2}\!\left(\tau\right), z - e_{3}\!\left(\tau\right)\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`WeierstrassP`	$\wp\!\left(z, \tau\right)$	Weierstrass elliptic function
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`CC`	$\mathbb{C}$	Complex numbers
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("124339"),
    Formula(Where(Equal(WeierstrassP(f(z), tau), z), Def(f(z), CarlsonRF(Sub(z, EllipticRootE(1, tau)), Sub(z, EllipticRootE(2, tau)), Sub(z, EllipticRootE(3, tau)))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

Fungrim entry: 124339

Topics using this entry