3 j , 6 j , 9 j Symbols - 34.2 Definition: Symbol

From testwiki
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
34.2.E1 | j r - j s | ≀ j t subscript 𝑗 π‘Ÿ subscript 𝑗 𝑠 subscript 𝑗 𝑑 {\displaystyle{\displaystyle|j_{r}-j_{s}|\leq j_{t}}}
|j_{r}-j_{s}| \leq j_{t}		 

abs(j[r]- j[s]) <= j[t]
 
Abs[Subscript[j, r]- Subscript[j, s]] <= Subscript[j, t]
 Skipped - no semantic math Skipped - no semantic math - -
34.2.E3 m 1 + m 2 + m 3 = 0 subscript π‘š 1 subscript π‘š 2 subscript π‘š 3 0 {\displaystyle{\displaystyle m_{1}+m_{2}+m_{3}=0}}
m_{1}+m_{2}+m_{3} = 0		 

m[1]+ m[2]+ m[3] = 0
 
Subscript[m, 1]+ Subscript[m, 2]+ Subscript[m, 3] == 0
 Skipped - no semantic math Skipped - no semantic math - -
34.2.E4 3 ⁒ j ⁒ j 1 ⁒ j 2 ⁒ j 3 ⁒ m 1 ⁒ m 2 ⁒ m 3 = ( - 1 ) j 1 - j 2 - m 3 ⁒ Ξ” ⁒ ( j 1 ⁒ j 2 ⁒ j 3 ) ⁒ ( ( j 1 + m 1 ) ! ⁒ ( j 1 - m 1 ) ! ⁒ ( j 2 + m 2 ) ! ⁒ ( j 2 - m 2 ) ! ⁒ ( j 3 + m 3 ) ! ⁒ ( j 3 - m 3 ) ! ) 1 2 ⁒ βˆ‘ s ( - 1 ) s s ! ⁒ ( j 1 + j 2 - j 3 - s ) ! ⁒ ( j 1 - m 1 - s ) ! ⁒ ( j 2 + m 2 - s ) ! ⁒ ( j 3 - j 2 + m 1 + s ) ! ⁒ ( j 3 - j 1 - m 2 + s ) ! threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript π‘š 1 subscript π‘š 2 subscript π‘š 3 superscript 1 subscript 𝑗 1 subscript 𝑗 2 subscript π‘š 3 Ξ” subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 superscript subscript 𝑗 1 subscript π‘š 1 subscript 𝑗 1 subscript π‘š 1 subscript 𝑗 2 subscript π‘š 2 subscript 𝑗 2 subscript π‘š 2 subscript 𝑗 3 subscript π‘š 3 subscript 𝑗 3 subscript π‘š 3 1 2 subscript 𝑠 superscript 1 𝑠 𝑠 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 𝑠 subscript 𝑗 1 subscript π‘š 1 𝑠 subscript 𝑗 2 subscript π‘š 2 𝑠 subscript 𝑗 3 subscript 𝑗 2 subscript π‘š 1 𝑠 subscript 𝑗 3 subscript 𝑗 1 subscript π‘š 2 𝑠 {\displaystyle{\displaystyle\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{% 3}}={(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1% }-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{% \frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!% (j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!}}}
\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!}		 

Error

ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3])*((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*((Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!*(Subscript[j, 3]- Subscript[m, 3])!)^(Divide[1,2])* Sum[Divide[(- 1)^(s),(s)!*(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3]- s)!*(Subscript[j, 1]- Subscript[m, 1]- s)!*(Subscript[j, 2]+ Subscript[m, 2]- s)!*(Subscript[j, 3]- Subscript[j, 2]+ Subscript[m, 1]+ s)!*(Subscript[j, 3]- Subscript[j, 1]- Subscript[m, 2]+ s)!], {s, - Infinity, Infinity}, GenerateConditions->None]
Missing Macro Error Translation Error - -
34.2.E6 3 ⁒ j ⁒ j 1 ⁒ j 2 ⁒ j 3 ⁒ m 1 ⁒ m 2 ⁒ m 3 = ( - 1 ) j 2 - m 1 + m 3 ⁒ ( j 1 + j 2 + m 3 ) ! ⁒ ( j 2 + j 3 - m 1 ) ! Ξ” ⁒ ( j 1 ⁒ j 2 ⁒ j 3 ) ⁒ ( j 1 + j 2 + j 3 + 1 ) ! ⁒ ( ( j 1 + m 1 ) ! ⁒ ( j 3 - m 3 ) ! ( j 1 - m 1 ) ! ⁒ ( j 2 + m 2 ) ! ⁒ ( j 2 - m 2 ) ! ⁒ ( j 3 + m 3 ) ! ) 1 2 ⁒ F 2 3 ⁑ ( - j 1 - j 2 - j 3 - 1 , - j 1 + m 1 , - j 3 - m 3 ; - j 1 - j 2 - m 3 , - j 2 - j 3 + m 1 ; 1 ) threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript π‘š 1 subscript π‘š 2 subscript π‘š 3 superscript 1 subscript 𝑗 2 subscript π‘š 1 subscript π‘š 3 subscript 𝑗 1 subscript 𝑗 2 subscript π‘š 3 subscript 𝑗 2 subscript 𝑗 3 subscript π‘š 1 Ξ” subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 1 superscript subscript 𝑗 1 subscript π‘š 1 subscript 𝑗 3 subscript π‘š 3 subscript 𝑗 1 subscript π‘š 1 subscript 𝑗 2 subscript π‘š 2 subscript 𝑗 2 subscript π‘š 2 subscript 𝑗 3 subscript π‘š 3 1 2 Gauss-hypergeometric-pFq 3 2 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 1 subscript 𝑗 1 subscript π‘š 1 subscript 𝑗 3 subscript π‘š 3 subscript 𝑗 1 subscript 𝑗 2 subscript π‘š 3 subscript 𝑗 2 subscript 𝑗 3 subscript π‘š 1 1 {\displaystyle{\displaystyle\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{% 3}}={(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{% \Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}% -m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{% \frac{1}{2}}\*{{{}_{3}F_{2}}\left(-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{% 3};-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1};1\right)}}}
\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\genhyperF{3}{2}@{-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3}}{-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1}}{1}}		 

Error

ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 2]- Subscript[m, 1]+ Subscript[m, 3])*Divide[(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[m, 3])!*(Subscript[j, 2]+ Subscript[j, 3]- Subscript[m, 1])!,((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!]*(Divide[(Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 3]- Subscript[m, 3])!,(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!])^(Divide[1,2])*HypergeometricPFQ[{- Subscript[j, 1]- Subscript[j, 2]- Subscript[j, 3]- 1 , - Subscript[j, 1]+ Subscript[m, 1], - Subscript[j, 3]- Subscript[m, 3]}, {- Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3], - Subscript[j, 2]- Subscript[j, 3]+ Subscript[m, 1]}, 1]
Missing Macro Error Translation Error - -
Retrieved from "https://lct.wmflabs.org/w/index.php?title=34.2&oldid=58558"