Fungrim entry: f35a37

E\!\left(\phi, 1\right) = {\left(-1\right)}^{\left\lfloor \operatorname{Re}(\phi) / \pi + 1 / 2 \right\rfloor} \sin(\phi) + 2 \left\lfloor \frac{\operatorname{Re}(\phi)}{\pi} + \frac{1}{2} \right\rfloor

Assumptions:

\phi \in \mathbb{C}

TeX:

E\!\left(\phi, 1\right) = {\left(-1\right)}^{\left\lfloor \operatorname{Re}(\phi) / \pi + 1 / 2 \right\rfloor} \sin(\phi) + 2 \left\lfloor \frac{\operatorname{Re}(\phi)}{\pi} + \frac{1}{2} \right\rfloor

\phi \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`IncompleteEllipticE`	$E\!\left(\phi, m\right)$	Legendre incomplete elliptic integral of the second kind
`Pow`	${a}^{b}$	Power
`Re`	$\operatorname{Re}(z)$	Real part
`Pi`	$\pi$	The constant pi (3.14...)
`Sin`	$\sin(z)$	Sine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f35a37"),
    Formula(Equal(IncompleteEllipticE(phi, 1), Add(Mul(Pow(-1, Floor(Add(Div(Re(phi), Pi), Div(1, 2)))), Sin(phi)), Mul(2, Floor(Add(Div(Re(phi), Pi), Div(1, 2))))))),
    Variables(phi),
    Assumptions(Element(phi, CC)))

Topics using this entry

Legendre elliptic integrals