SKEDSOFT

Bessel function of Second Kind:

The Bessel function of the second kind, Y_ν(x) is sometimes referred to as a Weber function or a Neumann function (which can be denoted as N_ν(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, J_v, J_-v are not linearly independent.

in which case Y_ν is needed to provide the second linearly independent solution of Bessel’s equation. In contrast, for non-integer orders, J_ν and J_−ν are linearly independent and Y_ν 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: