Examining the asymptotic forms, we see that two particular complex
linear combinations of the stationary solution have the behavior, at
infinity, of an outgoing or incoming spherical wave when the time
dependence is restored:

(13.28) | |||

(13.29) |

the

(13.30) | |||

(13.31) |

at infinity. Two particularly useful spherical hankel functions to know are the zeroth order ones:

(13.32) | |||

(13.33) |