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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving two Clebsch Gordan coefficients and one 6j symbol





http://functions.wolfram.com/07.38.23.0041.01









  


  










Input Form





Sum[(-1)^(2 e) ((Sqrt[2 a + 1] (2 c + 1))/Sqrt[2 b + 1]) ClebschGordan[{f, \[CurlyPhi]}, {c, \[Gamma]}, {b, \[Beta]}] ClebschGordan[{c, \[Gamma]}, {a, \[Alpha]}, {e, \[Epsilon]}] SixJSymbol[{c, f, b}, {d, e, a}], {c, Max[Abs[a - e], Abs[b - f]], Min[a + e, b + f]}, {\[Gamma], -c, c}] == ClebschGordan[{d, \[Delta]}, {b, \[Beta]}, {e, \[Epsilon]}] ClebschGordan[{f, \[CurlyPhi]}, {d, \[Delta]}, {a, \[Alpha]}]










Standard Form





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MathML Form







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</ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </lowlimit> <uplimit> <ci> c </ci> </uplimit> <apply> <sum /> <bvar> <ci> c </ci> </bvar> <lowlimit> <apply> <max /> <apply> <abs /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> </apply> </apply> <apply> <abs /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> </apply> </apply> </lowlimit> <uplimit> <apply> <min /> <apply> <plus /> <ci> a </ci> <ci> e </ci> </apply> <apply> <plus /> <ci> b </ci> <ci> f </ci> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> f </ci> <ci> &#966; 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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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