The function \(K _ { \nu } ( x )\) is the solution of the equation \(x ^ { 2 } y ^ { \prime \prime } + x y ^ { \prime } - ( x ^ { 2 } + \nu ^ { 2 } ) y = 0\) that diverges when \(x \to 0\) . Find the asymptotic behavior for small x for \(\nu \neq 0\) What happens for \(\nu = 0 ?\) For the sake of completeness, \(K _ { \nu } ( x )\) is called modified Bessel function of the second kind.
Small-$x$ asymptotics of the modified Bessel function $K_\nu$
P-TRIV-DE26
- Area
- Prelim
- Status
- draft