You are using the new UI (Beta).Return to the original UI

This page has been automatically translated by machine translation. Please note that translations may not be entirely accurate.

keisanHigh-precision calculations for everyday life and work
Login|Register

First-Order Derivatives of the First-Kind Kelvin Function (Graph)

TOP/Special functions/Kelvin function
Manage Bookmarks
Calculates a table and plots the first derivatives of the Kelvin functions of the first kind, ber'v(x) and bei'v(x).
Order v
Real numbers
[ Initial values for x
]
\(\normalsize Derivative\ Kelvin\ functions\\ \hspace{60px} of\ the\ 1st\ kind ber_\nu'(x),\ bei_\nu'(x)\\ (1)\ x^2y''+xy'-(ix^2+\nu^2)y=0\\ \hspace{25px} y=c_1{ber_\nu(x)}+ic_2{bei_\nu(x)}\\ (2)\ ber_\nu'(x)={\large\frac{ber_{\nu\tiny +1}(x)+bei_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}ber_\nu(x)\\ \hspace{25px} bei_\nu'(x)={\large\frac{bei_{\nu\tiny +1}(x)-ber_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}bei_\nu(x)\\\)

No customer feedback for this calculation yet.