ag-gipp/GoUldI

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data/mathematical/199.mml

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<math xmlns='http://www.w3.org/1998/Math/MathML' display='inline'><semantics><mrow><mrow><mo>{</mo><mrow><mtable displaystyle="false" rowspacing="0.5ex" rowlines="none"><mtr><mtd><msub><mi>j</mi> <mn>1</mn></msub></mtd> <mtd><msub><mi>j</mi> <mn>2</mn></msub></mtd> <mtd><msub><mi>j</mi> <mn>3</mn></msub></mtd></mtr> <mtr><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd> <mtd><msub><mi>j</mi> <mn>3</mn></msub><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd> <mtd><msub><mi>j</mi> <mn>2</mn></msub><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>=</mo><mo stretchy="false">(</mo><mo lspace="verythinmathspace" rspace="0em">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo> <mi>J</mi></msup><msup><mrow><mo>(</mo><mfrac><mrow><mo stretchy="false">(</mo><msub><mi>j</mi> <mn>2</mn></msub><mo>+</mo><msub><mi>j</mi> <mn>3</mn></msub><mo>−</mo><msub><mi>j</mi> <mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mi>j</mi> <mn>1</mn></msub><mo>+</mo><msub><mi>j</mi> <mn>2</mn></msub><mo>+</mo><msub><mi>j</mi> <mn>3</mn></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn><msub><mi>j</mi> <mn>2</mn></msub><mo stretchy="false">(</mo><mn>2</mn><msub><mi>j</mi> <mn>2</mn></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mn>2</mn><msub><mi>j</mi> <mn>3</mn></msub><mo stretchy="false">(</mo><mn>2</mn><msub><mi>j</mi> <mn>3</mn></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mfrac><mo>)</mo></mrow> <mfrac><mn>1</mn><mn>2</mn></mfrac></msup></mrow><annotation encoding='application/x-tex'>\begin{Bmatrix}j_{1}&j_{2}&j_{3}\\
\frac{1}{2}&j_{3}-\frac{1}{2}&j_{2}-\frac{1}{2}\end{Bmatrix}=(-1)^{J}\left(\frac{(j_{2}+j_{3}-j_{1})(j_{1}+j_{2}+j_{3}+1)}{2j_{2}(2j_{2}+1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</annotation></semantics></math>