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Statements
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ln
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arccos
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ln
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,
superscript
superscript
𝛼
2
𝜂
1
2
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2
𝛼
𝜂
𝛼
superscript
superscript
𝛼
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𝜂
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𝛼
𝑥
superscript
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superscript
𝛼
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1
2
𝛼
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1
superscript
𝛼
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superscript
𝛼
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superscript
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𝛼
𝑥
superscript
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superscript
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superscript
𝑥
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superscript
𝛼
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superscript
𝑥
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{\displaystyle{\displaystyle{\left(\alpha^{2}+\eta\right)^{1/2}+\tfrac{1}{2}%
\alpha\ln\eta-\alpha\ln\left(\left(\alpha^{2}+\eta\right)^{1/2}+\alpha\right)}%
={\operatorname{arccos}\left(\frac{x}{\left(1+\alpha^{2}\right)^{1/2}}\right)+%
\frac{\alpha}{2}\ln\left(\frac{1+\alpha^{2}+\left(\alpha^{2}-1\right)x^{2}-2%
\alpha x\left(1+\alpha^{2}-x^{2}\right)^{1/2}}{\left(1+\alpha^{2}\right)\left(%
1-x^{2}\right)}\right)},}}
arccos
z
𝑧
{\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
