Bessel function of the second kind
= Bessel function of the second kind
{c}
{title2=$Y_\nu(z)$}
For noninteger order, $Y_\nu=(\cos(\pi\nu)J_\nu-J_{-\nu})/\sin(\pi\nu)$; the integer-order function is defined by a limit. It gives a second independent solution of the <Bessel differential equation>. At order zero, $Y_0(z)\sim(2/\pi)[\log(z/2)+\gamma]$ near positive zero and $Y_0(z)\sim\sqrt{2/(\pi z)}\sin(z-\pi/4)$ at large positive argument, where $\gamma$ is the <Euler--Mascheroni constant>.