34.2: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/34.2.E1 34.2.E1] || [[Item:Q9710|<math>|j_{r}-j_{s}| \leq j_{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>|j_{r}-j_{s}| \leq j_{t}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">abs(j[r]- j[s]) <= j[t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Abs[Subscript[j, r]- Subscript[j, s]] <= Subscript[j, t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/34.2.E1 34.2.E1] || <math qid="Q9710">|j_{r}-j_{s}| \leq j_{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>|j_{r}-j_{s}| \leq j_{t}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">abs(j[r]- j[s]) <= j[t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Abs[Subscript[j, r]- Subscript[j, s]] <= Subscript[j, t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/34.2.E3 34.2.E3] || [[Item:Q9712|<math>m_{1}+m_{2}+m_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m_{1}+m_{2}+m_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m[1]+ m[2]+ m[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[m, 1]+ Subscript[m, 2]+ Subscript[m, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/34.2.E3 34.2.E3] || <math qid="Q9712">m_{1}+m_{2}+m_{3} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m_{1}+m_{2}+m_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m[1]+ m[2]+ m[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[m, 1]+ Subscript[m, 2]+ Subscript[m, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/34.2.E4 34.2.E4] || [[Item:Q9713|<math>\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)!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Translation Error || - || -
| [https://dlmf.nist.gov/34.2.E4 34.2.E4] || <math qid="Q9713">\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)!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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)!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Translation Error || - || -
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| [https://dlmf.nist.gov/34.2.E6 34.2.E6] || [[Item:Q9715|<math>\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}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Translation Error || - || -
| [https://dlmf.nist.gov/34.2.E6 34.2.E6] || <math qid="Q9715">\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}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Translation Error || - || -
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Latest revision as of 12:14, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
34.2.E1 | j r - j s | ≤ j t subscript 𝑗 𝑟 subscript 𝑗 𝑠 subscript 𝑗 𝑡 {\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 𝑚 1 subscript 𝑚 2 subscript 𝑚 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 ⁢ Δ ⁢ ( 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 ⁢ ∑ 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 𝑚 1 subscript 𝑚 2 subscript 𝑚 3 superscript 1 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 3 Δ subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 superscript 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 1 2 subscript 𝑠 superscript 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 {\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 ) ! Δ ⁢ ( 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 𝑚 1 subscript 𝑚 2 subscript 𝑚 3 superscript 1 subscript 𝑗 2 subscript 𝑚 1 subscript 𝑚 3 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 3 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 Δ subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 1 superscript 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 1 2 Gauss-hypergeometric-pFq 3 2 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 {\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 - -
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