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Statements
ζ
^
=
-
(
3
2
κ
(
-
1
2
X
+
2
μ
arctan
(
x
κ
-
x
κ
2
-
μ
2
-
2
μ
2
μ
X
)
+
κ
arccos
(
x
-
2
κ
2
κ
2
-
μ
2
)
)
)
2
/
3
,
^
𝜁
superscript
3
2
𝜅
1
2
𝑋
2
𝜇
𝑥
𝜅
𝑥
superscript
𝜅
2
superscript
𝜇
2
2
superscript
𝜇
2
𝜇
𝑋
𝜅
𝑥
2
𝜅
2
superscript
𝜅
2
superscript
𝜇
2
2
3
{\displaystyle{\displaystyle\widehat{\zeta}=-\left(\frac{3}{2\kappa}\left(-%
\frac{1}{2}X+2\mu\operatorname{arctan}\left(\frac{x\kappa-x\sqrt{\kappa^{2}-%
\mu^{2}}-2\mu^{2}}{\mu X}\right)+\kappa\operatorname{arccos}\left(\frac{x-2%
\kappa}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)\right)\right)^{2/3},}}
2
κ
-
2
κ
2
-
μ
2
<
x
≤
2
κ
+
2
κ
2
-
μ
2
2
𝜅
2
superscript
𝜅
2
superscript
𝜇
2
𝑥
2
𝜅
2
superscript
𝜅
2
superscript
𝜇
2
{\displaystyle{\displaystyle 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}<x\leq 2\kappa+%
2\sqrt{\kappa^{2}-\mu^{2}}}}
arccos
z
𝑧
{\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
arctan
z
𝑧
{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
X
𝑋
{\displaystyle{\displaystyle X}}
Identifiers
