# Kelvin function of the 1st kind Calculator

## Calculates the Kelvin functions of the first kind berv(x) and beiv(x), and their derivatives ber'v(x) and bei'v(x).

 order v real number x complex number 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Kelvin\ functions\\\hspace{60} of\ the\ 1st\ kind\ ber_\nu(x),\ bei_\nu(x)\\[10](1)\ x^2y''+xy'-(ix^2+\nu^2)y=0\\\hspace{25} y=c_1{ber_\nu(x)}+ic_2{bei_\nu(x)}\\[10](2)\ ber_\nu(x)+ibei_\nu(x)=J_\nu(x{\large e^{i\frac{3\pi}{4}}})\\\hspace{80}={\large(\frac{x}{2})^\nu e^{i\frac{3\nu\pi}{4}}\sum_{\small k=0}^{\small\infty}\frac{(\frac{ix^2}{4})^{k}}{k!\Gamma(\nu+k+1)}}\\[10](3)\ ber_\nu'(x)={\large\frac{ber_{\nu\tiny +1}(x)+bei_{\nu\tiny +1}(x)}{\sqrt{2}}}+{\large\frac{\nu}{x}}ber_\nu(x)\\\hspace{25} bei_\nu'(x)={\large\frac{bei_{\nu\tiny +1}(x)-ber_{\nu\tiny +1}(x)}{\sqrt{2}}}+{\large\frac{\nu}{x}}bei_\nu(x)\\$

Kelvin function of the 1st kind
 [1-6] /6 Disp-Num5103050100200
[1]  2018/03/19 21:27   Male / 50 years old level / An office worker / A public employee / Very /
Purpose of use
Calculation software verification
[2]  2014/02/16 14:47   Male / 30 years old level / An engineer / A little /
Purpose of use
I want to use it fro ASME part UHX calculation.
Comment/Request
Can you please provide graphs also? If I want to find them at relative value of X i have to go through most values and to do a maxima and minina in a fixed domain.
from Keisan
Please refer to Kelvin function of the 1st kind (chart) Calculator
[3]  2012/04/24 03:28   Male / 30 years old level / A student / Very /
Comment/Request
You can also write your own code to calculate kelvin functions.Handbook of mathematical function will be very useful.
[4]  2010/04/05 06:31   Male / 20 level / A university student / Very /
Purpose of use
To check numerical code
Comment/Request
[5]  2010/03/07 19:32   Male / More than 60 / A researcher / Very /
Purpose of use
Calculations on an induction furnace
Comment/Request
A most useful tool in connection with calculatoons on induction heating problems.
[6]  2009/04/09 16:48   Male / 30 level / A researcher / Very /
Purpose of use
Calculation of Kelvin function
Comment/Request

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