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Fungrim entry: 713966

K ⁣(m‾)=K(m)‾K\!\left(\overline{m}\right) = \overline{K(m)}
Assumptions:m∈C∖(1,∞)m \in \mathbb{C} \setminus \left(1, \infty\right)
TeX:
K\!\left(\overline{m}\right) = \overline{K(m)}

m \in \mathbb{C} \setminus \left(1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Conjugatez‾\overline{z} Complex conjugate
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("713966"),
    Formula(Equal(EllipticK(Conjugate(m)), Conjugate(EllipticK(m)))),
    Variables(m),
    Assumptions(Element(m, SetMinus(CC, OpenInterval(1, Infinity)))))

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