ag-gipp/GoUldI

<math xmlns='http://www.w3.org/1998/Math/MathML' display='inline'><semantics><mrow><mrow><msup><mrow><mo>(</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>+</mo><mi>η</mi><mo>)</mo></mrow> <mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><mo>+</mo><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mi>α</mi><mi>ln</mi><mi>η</mi><mo>−</mo><mi>α</mi><mi>ln</mi><mrow><mo>(</mo><msup><mrow><mo>(</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>+</mo><mi>η</mi><mo>)</mo></mrow> <mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>α</mi><mo>)</mo></mrow></mrow><mo>=</mo><mrow><mi><mrow><mi>a</mi><mi>r</mi><mi>c</mi><mi>c</mi><mi>o</mi><mi>s</mi></mrow></mi><mrow><mo>(</mo><mfrac><mi>x</mi><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>)</mo></mrow> <mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mfrac><mi>α</mi><mn>2</mn></mfrac><mi>ln</mi><mrow><mo>(</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>+</mo><mrow><mo>(</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><msup><mi>x</mi> <mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>α</mi><mi>x</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>−</mo><msup><mi>x</mi> <mn>2</mn></msup><mo>)</mo></mrow> <mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>α</mi> <mn>2</mn></msup><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mi>x</mi> <mn>2</mn></msup><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><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>