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Confusion with Hankel functions
I believe 1st and 2nd kind of Hankel functions on this page should be switched. It is hℓ(1) that behaves as eikr/(kr) and is thus an outgoing wave, and not hℓ(2). See e.g. Abramowitz and Stegun (10.1.16) and (10.1.17) or Eq. (2.52) in arXiv:2306.05395.