Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta:   an Elementary Method
  Yu and Littlejohn recently studied in arXiv:1104.1499 some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j, 12j and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano-Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron is needed, leading to new asymptotics for Wigner 3nj-symbols. As an illustration, we present 15j-symbols with one, two and four small angular momenta, and give an alternative formula to Yu's recent 15j-symbol with three small spins. 
Valentin Bonzom and Pierre Fleury
quant-ph gr-qc math-ph math.MP