Third-Kind Kelvin Functions
Calculates the Kelvin functions of the third kind, herv(x) and heiv(x), and their derivatives her'v(x) and hei'v(x).
| \(\normalsize Kelvin\ functions\\ \hspace{60px} of\ the\ 3rd\ kind\ her_\nu(x),\ hei_\nu(x)\\ (1)\ x^2y''+xy'-(ix^2+\nu^2)y=0\\ \hspace{25px} y=c_1{her_\nu(x)}+ic_2{hei_\nu(x)}\\ (2)\ her_\nu(x)+ihei_\nu(x)=H^{(1)}_\nu(x{\large e^{i\frac{3\pi}{4}}})\\ \hspace{135px}={\large\frac{2}{i\pi}}\left(ker_\nu(x)+ikei_\nu(x)\right)\\ (3)\ her_\nu'(x)={\large\frac{her_{\nu\tiny +1}(x)+hei_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}her_\nu(x)\\ \hspace{25px}hei_\nu'(x)={\large\frac{hei_{\nu\tiny +1}(x)-her_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}hei_\nu(x)\\\) |
No customer feedback for this calculation yet.