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Pb. 2.26 The recursion relations can, in addition to defining orthogonal
polynomials, also define some special functions of mathematical physics. For
example, the spherical Bessel functions that play an important role in defin-
ing the modes of spherical cavities in electrodynamics and scattering ampli-
tudes in both classical and quantum physics are defined through the
following recursion relation:

+
x =
x −
j ()  32 m j () j x ()
m+2  x  m+1 m
With
x −
jx = sin( x) − cos( x) and jx =  3 − 1  sin( ) 3cos( x)
( )
()
1 2 2  3 x  2
x x  x x
Plot j (x) over the interval 0 < x < 15.
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