Bessel function of Second Kind
Bessel function of Second Kind:
The Bessel function of the second kind, Yν(x) is sometimes referred to as a Weber function or a Neumann function (which can be denoted as Nν(x)). It is related to the Bessel function of the first kind as follows:
Where we talk the limit v →n for integer value of v.
For integer order v, Jv, J-v are not linearly independent.
in which case Yν is needed to provide the second linearly independent solution of Bessel’s equation. In contrast, for non-integer orders, Jν and J−ν are linearly independent and Yν is redundant. The Bessel function of the second kind of order ν can be expressed in terms of the Bessel function of the first kind as follows: