mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="left-parenthesis alpha squared plus eta right-parenthesis Superscript 1 slash 2 Baseline plus one-half alpha ln eta minus alpha ln left-parenthesis left-parenthesis alpha squared plus eta right-parenthesis Superscript 1 slash 2 Baseline plus alpha right-parenthesis equals arc cosine left-parenthesis StartFraction x Over left-parenthesis 1 plus alpha squared right-parenthesis Superscript 1 slash 2 Baseline EndFraction right-parenthesis plus StartFraction alpha Over 2 EndFraction ln left-parenthesis StartFraction 1 plus alpha squared plus left-parenthesis alpha squared minus 1 right-parenthesis x squared minus 2 alpha x left-parenthesis 1 plus alpha squared minus x squared right-parenthesis Superscript 1 slash 2 Baseline Over left-parenthesis 1 plus alpha squared right-parenthesis left-parenthesis 1 minus x squared right-parenthesis EndFraction right-parenthesis">
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<annotation encoding="application/x-tex">{\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)}</annotation>
</semantics>
</math>