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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Integral representations > Multiple integral representations > Involving the direct function





http://functions.wolfram.com/07.38.07.0009.01









  


  








Input Form





Abs[ClebschGordan[{Subscript[j, 1], 0}, {Subscript[j, 2], 0}, {j, 0}]]^2 == ((2 j + 1)/2) Integrate[Sin[\[CurlyTheta]] LegendreP[Subscript[j, 1], Cos[\[CurlyTheta]]] LegendreP[Subscript[j, 2], Cos[\[CurlyTheta]]] LegendreP[j, Cos[\[CurlyTheta]]], {\[CurlyTheta], 0, Pi}] /; Element[Subscript[j, 1], Integers] && Subscript[j, 1] >= 0 && Element[Subscript[j, 2], Integers] && Subscript[j, 2] >= 0 && Element[j, Integers] && j >= 0 && Abs[Subscript[j, 1] - Subscript[j, 2]] <= j <= Subscript[j, 1] + Subscript[j, 2]








Standard Form





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MathML Form







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</ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <pi /> </uplimit> <apply> <times /> <apply> <sin /> <ci> &#977; </ci> </apply> <apply> <ci> LegendreP </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <cos /> <ci> &#977; </ci> </apply> </apply> <apply> <ci> LegendreP </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cos /> <ci> &#977; </ci> </apply> </apply> <apply> <ci> LegendreP </ci> <ci> j </ci> <apply> <cos /> <ci> &#977; </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8469; </ci> </apply> <apply> <in /> <ci> j </ci> <ci> &#8469; </ci> </apply> <apply> <leq /> <apply> <abs /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <ci> j </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29