Quasiclassical asymptotic behavior for Wigner's $3j$-symbols

Expressions for Wigner's $3j$-symbols are considered which hold in the asymptotic limit of large quantum numbers of the angular momenta. It is shown that, depending on the quantum numbers of the angular momentum projections, there exist three types of expression: “classical”, “tunnel”, “transition”. Numerical calculations have been made of the values of definite $3j$-symbols in accordance with exact and approximate expressions, and these show that the expressions have a good accuracy already for angular momenta of order 5.