Please check out the book (Boas 12.12). For non integer p,
and
i.e., goes to
as r goes to
, and
goes to
as r goes to zero. For integer p,
i.e., is even for even p and odd for odd p. Check out all
the nice relations Boas p. 514. Spherical Bessel Functions same as
I's and K's can be found in Boas p. 517 - 518. Also:
General case Bessel Equation:
Solution:
with . Useful relations:
where a and b are zeros of .