Fungrim entry: 75e141

E\!\left(\phi, 1\right) = \sin(\phi)

Assumptions:

\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(\operatorname{Re}(\phi) \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right) \;\mathbin{\operatorname{or}}\; \phi = \frac{\pi}{2}\right)

TeX:

E\!\left(\phi, 1\right) = \sin(\phi)

\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(\operatorname{Re}(\phi) \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right) \;\mathbin{\operatorname{or}}\; \phi = \frac{\pi}{2}\right)

Definitions:

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

Source code for this entry:

Entry(ID("75e141"),
    Formula(Equal(IncompleteEllipticE(phi, 1), Sin(phi))),
    Variables(phi),
    Assumptions(And(Element(phi, CC), Or(Element(Re(phi), ClosedOpenInterval(Div(Neg(Pi), 2), Div(Pi, 2))), Equal(phi, Div(Pi, 2))))))

Topics using this entry

Legendre elliptic integrals