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  "body": "\n## Summary\n\nThe Bessel function of the second kind $Y_\\nu$ is a second solution of Bessel's equation, independent of the [[Bessel function of the first kind|CZCMRDWDYW]] $J_\\nu$.\nIt is also called the Weber function or the Neumann function, and it is sometimes written $N_\\nu$.\nUnlike $J_\\nu$, it is unbounded near $0$.\nTogether, $J_\\nu$ and $Y_\\nu$ span all solutions of [[Bessel's equation|EAV97QH9DF]].\n\n## Explanations\n\n### L1 human\n\nBessel's equation is of second order, so it needs two independent solutions.\nThe first kind $J_\\nu$ is the one that stays finite at the origin.\nThe second kind $Y_\\nu$ is the other one, and it blows up at the origin.\nFor example, $Y_0(x)$ behaves like $\\frac{2}{\\pi} \\ln x$ for small $x \u003e 0$.\nFor large $x$, both $J_\\nu$ and $Y_\\nu$ oscillate like shifted sine waves of slowly shrinking size.\n",
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