Operator Racah algebra and Laplace‐type expansions of irreducible spherical tensors

Differential formulas for coefficients in the Laplace‐type series of an arbitrary spherical tensor f L M (r+R) are given in terms of an operator N applied to the radial part φ(r) of f L M (r). Very compact and convenient expressions for N in terms of operator Pochhammer symbols are established. A special representation of the coefficients of the Laplace‐type series, in terms of the operator Gauss function 2 F 1, is given, which, in turn, provides a remarkably short proof of two earlier Sack expansions. More general gradient formulas are introduced and numerous particular cases of the Laplace‐type expansions are considered in detail.