DLMF:34.5.E11
type: Item
Digital Library of Mathematical Functions ID: 34.5.E11
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{(2j_{1}+1)\left((J_{3}+J_{2}-J_{1})(L_{3}+L_{2}-J% _{1})-2(J_{3}L_{3}+J_{2}L_{2}-J_{1}L_{1})\right)\mathit{6j}{j_{1}}{j_{2}}{j_{3% }}{l_{1}}{l_{2}}{l_{3}}}\\ =j_{1}E(j_{1}+1)\mathit{6j}{j_{1}+1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}+(j_{1}% +1)E(j_{1})\mathit{6j}{j_{1}-1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}},}}" display="inline"> ( 2 ⁢ j 1 + 1 ) ⁢ ( ( J 3 + J 2 - J 1 ) ⁢ ( L 3 + L 2 - J 1 ) - 2 ⁢ ( J 3 ⁢ L 3 + J 2 ⁢ L 2 - J 1 ⁢ L 1 ) ) ⁢ 6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 = j 1 ⁢ E ⁢ ( j 1 + 1 ) ⁢ 6 ⁢ j ⁢ j 1 + 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 + ( j 1 + 1 ) ⁢ E ⁢ ( j 1 ) ⁢ 6 ⁢ j ⁢ j 1 - 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 , <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.115.2.cmml" xref="p1.1.m1.1.115"> <eq id="p1.1.m1.1.62.cmml" xref="p1.1.m1.1.62"/> <apply id="p1.1.m1.1.115.2.1.cmml" xref="p1.1.m1.1.115.2.1"> <times id="p1.1.m1.1.115.2.1.1.cmml" xref="p1.1.m1.1.115.2.1.1"/> <apply id="p1.1.m1.1.115.2.1.2.2.cmml" xref="p1.1.m1.1.115.2.1.2"> <plus id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/> <apply id="p1.1.m1.1.115.2.1.2.2.1.cmml" xref="p1.1.m1.1.115.2.1.2.2.1"> <times id="p1.1.m1.1.115.2.1.2.2.1.1.cmml" xref="p1.1.m1.1.115.2.1.2.2.1.1"/> <cn type="integer" id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">2</cn> <apply id="p1.1.m1.1.115.2.1.2.2.1.2.cmml" xref="p1.1.m1.1.115.2.1.2.2.1.2"> <csymbol cd="ambiguous" id="p1.1.m1.1.115.2.1.2.2.1.2.1.cmml" xref="p1.1.m1.1.115.2.1.2.2.1.2">subscript</csymbol> <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑗</ci> <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">1</cn> </apply> </apply> <cn type="integer" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">1</cn> </apply> <apply id="p1.1.m1.1.115.2.1.3.2.cmml" xref="p1.1.m1.1.115.2.1.3"> <minus id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29"/> <apply id="p1.1.m1.1.115.2.1.3.2.1.cmml" xref="p1.1.m1.1.115.2.1.3.2.1"> <times id="p1.1.m1.1.115.2.…
Symbols used: $$\mathit{6j}$$ symbol
Symbols used: non-negative integers or non-negative integers plus one half.
Symbols used: J r
Symbols used: L r
Symbols used: 34.5.E13
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile