Assumptions:
TeX:
E\!\left(\phi, m\right) = \int_{0}^{\sin(\phi)} \frac{\sqrt{1 - m {x}^{2}}}{\sqrt{1 - {x}^{2}}} \, dx \phi \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \;\mathbin{\operatorname{and}}\; m \in \mathbb{C}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
IncompleteEllipticE | Legendre incomplete elliptic integral of the second kind | |
Integral | Integral | |
Sqrt | Principal square root | |
Pow | Power | |
Sin | Sine | |
ClosedInterval | Closed interval | |
Pi | The constant pi (3.14...) | |
CC | Complex numbers |
Source code for this entry:
Entry(ID("5e869b"), Formula(Equal(IncompleteEllipticE(phi, m), Integral(Div(Sqrt(Sub(1, Mul(m, Pow(x, 2)))), Sqrt(Sub(1, Pow(x, 2)))), For(x, 0, Sin(phi))))), Variables(phi, m), Assumptions(And(Element(phi, ClosedInterval(Div(Neg(Pi), 2), Div(Pi, 2))), Element(m, CC))))