The non-compact group O (2, 1) is used in an investigation of hydrogenic radial wavefunctions. These radial functions are shown to form bases for infinite dimensional representations of the algebra of O (2, 1). It is found that rN and r-N (N positive) transform as tensors with respect to this algebra. Analysis of matrix elements of rN and r-N shows that the Wigner-Eckart theorem is valid for this group and that the pertinent Clebsch-Gordan coefficients are proportional to the familiar R(3) Clebsch-Gordan coefficients. This proportionality provides simple explanations of the selection rules for hydrogenic radial matrix elements noted by Pasternack and Sternheimer, and the proportionality of hydrogenic expectation values of rN and r-N to 3 - j symbols