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SixJSymbol






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SixJSymbol[{j1,j2,j3},{j4,j5,j6}] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/07.40.26.0004.01









  


  










Input Form





SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == (-1)^(Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 5]) ((Sqrt[(Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(-Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(Subscript[j, 3] + Subscript[j, 4] - Subscript[j, 5])!] Sqrt[(Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(Subscript[j, 2] - Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(-Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(Subscript[j, 1] - Subscript[j, 5] + Subscript[j, 6])!] Sqrt[(-Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6])!] (1 + Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 5])!)/ (Sqrt[(Subscript[j, 1] + Subscript[j, 2] - Subscript[j, 3])!] Sqrt[(1 + Subscript[j, 1] + Subscript[j, 2] + Subscript[j, 3])!] Sqrt[(-Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(1 + Subscript[j, 3] + Subscript[j, 4] + Subscript[j, 5])!] Sqrt[(Subscript[j, 2] + Subscript[j, 4] - Subscript[j, 6])!] Sqrt[(Subscript[j, 1] + Subscript[j, 5] - Subscript[j, 6])!] Sqrt[(1 + Subscript[j, 2] + Subscript[j, 4] + Subscript[j, 6])!] Sqrt[(1 + Subscript[j, 1] + Subscript[j, 5] + Subscript[j, 6])!] (-Subscript[j, 1] + Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 6])! (-Subscript[j, 2] + Subscript[j, 3] - Subscript[j, 5] + Subscript[j, 6])!)) HypergeometricPFQ[ {-Subscript[j, 1] - Subscript[j, 2] + Subscript[j, 3], Subscript[j, 3] - Subscript[j, 4] - Subscript[j, 5], -Subscript[j, 1] - Subscript[j, 5] + Subscript[j, 6], -Subscript[j, 2] - Subscript[j, 4] + Subscript[j, 6]}, {-Subscript[j, 1] - Subscript[j, 2] - Subscript[j, 4] - Subscript[j, 5] - 1, -Subscript[j, 1] + Subscript[j, 3] - Subscript[j, 4] + Subscript[j, 6] + 1, -Subscript[j, 2] + Subscript[j, 3] - Subscript[j, 5] + Subscript[j, 6] + 1}, 1] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\ \[ScriptA]\[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-12-21





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