Expectation values of ${\mathit{r}}^{\mathit{P}}$ for an arbitrary nl hydrogenic state are expressed in terms of state-independent coefficients that are determined by a simple recursion relation. Explicit results are given for negative P down to -16 and, by an algebraic transformation, for positive P up to 13. Closed-form expressions are obtained for the coefficients of the two highest-order terms in l multiplying each power of n. The result is an asymptotic expression valid for each P and sufficiently large l.

• Received 16 March 1990

DOI:https://doi.org/10.1103/PhysRevA.42.1123