Spherical Bessel Function of the Second Kind

The spherical Bessel function of the second kind, denoted or , is defined by

(1)

where is a Bessel function of the second kind and, in general, and are complex numbers.

The spherical Bessel function of the second kind is implemented in the Wolfram Language as SphericalBesselY[n, z].

The function is most commonly encountered in the case a nonnegative integer, in which case, for , it is given by

			(2)
			(3)
			(4)

where is a Bessel function of the first kind, is the gamma function, and negative odd double factorials are defined by for nonnegative integers , with .

Specific cases for small nonnegative integer are given by

			(5)
			(6)
			(7)