3 j , 6 j , 9 j Symbols - 34.8 Approximations for Large Parameters
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 34.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\theta} = \frac{j_{1}(j_{1}+1)+j_{2}(j_{2}+1)-j_{3}(j_{3}+1)}{2\sqrt{j_{1}(j_{1}+1)j_{2}(j_{2}+1)}}}
\cos@@{\theta} = \frac{j_{1}(j_{1}+1)+j_{2}(j_{2}+1)-j_{3}(j_{3}+1)}{2\sqrt{j_{1}(j_{1}+1)j_{2}(j_{2}+1)}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(theta) = (j[1]*(j[1]+ 1)+ j[2]*(j[2]+ 1)- j[3]*(j[3]+ 1))/(2*sqrt(j[1]*(j[1]+ 1)*j[2]*(j[2]+ 1)))
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Cos[\[Theta]] == Divide[Subscript[j, 1]*(Subscript[j, 1]+ 1)+ Subscript[j, 2]*(Subscript[j, 2]+ 1)- Subscript[j, 3]*(Subscript[j, 3]+ 1),2*Sqrt[Subscript[j, 1]*(Subscript[j, 1]+ 1)*Subscript[j, 2]*(Subscript[j, 2]+ 1)]]
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Failure | Failure | Failed [300 / 300] Result: .2305430189-.3969495503*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, j[1] = 1/2*3^(1/2)+1/2*I, j[2] = 1/2*3^(1/2)+1/2*I, j[3] = 1/2*3^(1/2)+1/2*I}
Result: -.4524696831-.2139368486*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, j[1] = 1/2*3^(1/2)+1/2*I, j[2] = 1/2*3^(1/2)+1/2*I, j[3] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[0.23054301905722518, -0.39694955022903244]
Test Values: {Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-0.452469682834994, -0.2139368483368131]
Test Values: {Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |