The modified Bessel function of the second kind has the following integral representation: \(K _ { \nu } ( x ) = \frac { 1 } { 2 } \int _ { 0 } ^ { \infty } \exp \left( - \frac { x } { 2 } \left( s + \frac { 1 } { s } \right) \right) \frac { \mathrm { d } s } { s ^ { 1 - \nu } }\) . Find the asymptotic expansion for \(x \gg 1\)
Large-$x$ asymptotics of the modified Bessel function $K_\nu$
P-TRIV-CA27
- Area
- Complex Analysis
- Status
- draft