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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving four Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.23.0033.01









  


  










Input Form





Sum[(-1)^(c - \[Gamma] + e - \[Epsilon]) ClebschGordan[{a, \[Alpha]}, {b, \[Beta]}, {c, \[Gamma]}] ClebschGordan[{c, \[Gamma]}, {f, \[CurlyPhi]}, {j, \[Mu]}] ClebschGordan[{e, \[Epsilon]}, {b, \[Beta]}, {g, \[Eta]}] ClebschGordan[{d, \[Delta]}, {f, \[CurlyPhi]}, {e, \[Epsilon]}], {\[Beta], -b, b}, {\[Gamma], -c, c}, {\[Epsilon], -e, e}, {\[CurlyPhi], -f, f}] == (-1)^(a + d - \[Alpha] - \[Delta]) Sqrt[2 c + 1] Sqrt[2 e + 1] Sqrt[2 g + 1] Sqrt[2 j + 1] Sum[ClebschGordan[{g, \[Eta]}, {j, -\[Mu]}, {k, \[Kappa]}] ClebschGordan[{d, \[Delta]}, {a, -\[Alpha]}, {k, \[Kappa]}] NineJSymbol[{c, b, a}, {f, e, d}, {j, g, k}], {k, Max[Abs[g - j], Abs[a - d]], Min[g + j, a + d]}, {\[Kappa], -k, k}]










Standard Form





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MathML Form







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</mo> <mrow> <mo> { </mo> <mtable> <mtr> <mtd> <mi> c </mi> </mtd> <mtd> <mi> b </mi> </mtd> <mtd> <mi> a </mi> </mtd> </mtr> <mtr> <mtd> <mi> f </mi> </mtd> <mtd> <mi> e </mi> </mtd> <mtd> <mi> d </mi> </mtd> </mtr> <mtr> <mtd> <mi> j </mi> </mtd> <mtd> <mi> g </mi> </mtd> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> } </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> &#966; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </lowlimit> <uplimit> <ci> f </ci> </uplimit> <apply> <sum /> <bvar> <ci> &#1013; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> </lowlimit> <uplimit> <ci> e </ci> </uplimit> <apply> <sum /> <bvar> <ci> &#947; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </lowlimit> <uplimit> <ci> c </ci> </uplimit> <apply> <sum /> <bvar> <ci> &#946; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </lowlimit> <uplimit> <ci> b </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> c </ci> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#947; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#1013; </ci> </apply> </apply> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> a </ci> <ci> &#945; </ci> </list> <list> <ci> b </ci> <ci> &#946; </ci> </list> <list> <ci> c </ci> <ci> &#947; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> c </ci> <ci> &#947; </ci> </list> <list> <ci> f </ci> <ci> &#966; </ci> </list> <list> <ci> j </ci> <ci> &#956; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> e </ci> <ci> &#1013; </ci> </list> <list> <ci> b </ci> <ci> &#946; </ci> </list> <list> <ci> g </ci> <ci> &#951; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> d </ci> <ci> &#948; </ci> </list> <list> <ci> f </ci> <ci> &#966; </ci> </list> <list> <ci> e </ci> <ci> &#1013; </ci> </list> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#948; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> &#954; </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <apply> <max /> <apply> <abs /> <apply> <plus /> <ci> g </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <abs /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> </apply> </apply> </lowlimit> <uplimit> <apply> <min /> <apply> <plus /> <ci> g </ci> <ci> j </ci> </apply> <apply> <plus /> <ci> a </ci> <ci> d </ci> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> ClebschGordan </ci> <list> <ci> g </ci> <ci> &#951; </ci> </list> <list> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </list> <list> <ci> k </ci> <ci> &#954; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> d </ci> <ci> &#948; </ci> </list> <list> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </list> <list> <ci> k </ci> <ci> &#954; </ci> </list> </apply> <list> <list> <list> <ci> c </ci> <ci> b </ci> <ci> a </ci> </list> <list> <ci> f </ci> <ci> e </ci> <ci> d </ci> </list> <list> <ci> j </ci> <ci> g </ci> <ci> k </ci> </list> </list> </list> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-12-21





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