# 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC