# Kelvin function of the 2nd kind Calculator

## Calculates the Kelvin functions of the second kind kerv(x) and keiv(x), and their derivatives ker'v(x) and kei'v(x).

order v
 real number
x
 complex number
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Kelvin\ functions\\\hspace{60}of\ the\ 2nd\ kind\ ker_\nu(x),\ kei_\nu(x)\\[10](1)\ x^2y''+xy'-(ix^2+\nu^2)y=0\\\hspace{25} y=c_1{ker_\nu(x)}+ic_2{kei_\nu(x)}\\[10](2)\ ker_\nu(x)+ikei_\nu(x)={\large e^{-i\frac{\nu\pi}{2}}}K_\nu(x{\large e^{i\frac{\pi}{4}}})\\[10](3)\ ker_\nu'(x)={\large\frac{ker_{\nu\tiny +1}(x)+kei_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}ker_\nu(x)\\\hspace{25} kei_\nu'(x)={\large\frac{kei_{\nu\tiny +1}(x)-ker_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}kei_\nu(x)\\$

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