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Statements
1
2
ζ
(
ζ
2
-
α
2
)
1
/
2
-
1
2
α
2
arccosh
(
ζ
α
)
=
(
1
-
a
2
)
1
/
2
arctanh
(
1
x
(
x
2
-
a
2
1
-
a
2
)
1
/
2
)
-
arccosh
(
x
a
)
,
1
2
𝜁
superscript
superscript
𝜁
2
superscript
𝛼
2
1
2
1
2
superscript
𝛼
2
hyperbolic-inverse-cosine
𝜁
𝛼
superscript
1
superscript
𝑎
2
1
2
hyperbolic-inverse-tangent
1
𝑥
superscript
superscript
𝑥
2
superscript
𝑎
2
1
superscript
𝑎
2
1
2
hyperbolic-inverse-cosine
𝑥
𝑎
{\displaystyle{\displaystyle\frac{1}{2}\zeta\left(\zeta^{2}-\alpha^{2}\right)^%
{1/2}-\frac{1}{2}\alpha^{2}\operatorname{arccosh}\left(\frac{\zeta}{\alpha}%
\right)=\left(1-a^{2}\right)^{1/2}\operatorname{arctanh}\left(\frac{1}{x}\left%
(\frac{x^{2}-a^{2}}{1-a^{2}}\right)^{1/2}\right)-\operatorname{arccosh}\left(%
\frac{x}{a}\right),}}
α
≤
ζ
<
∞
𝛼
𝜁
{\displaystyle{\displaystyle\alpha\leq\zeta<\infty}}
arccosh
z
hyperbolic-inverse-cosine
𝑧
{\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
arctanh
z
hyperbolic-inverse-tangent
𝑧
{\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
a
𝑎
{\displaystyle{\displaystyle a}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
Identifiers
