# Modified Bessel function of the 1st kind (chart) Calculator

## Calculates a table of the modified Bessel function of the first kind Iv(x) and draws the chart.

 order v real number [ initial value x increment repetition ]
 $\normal Modified\ Bessel\ function\\\hspace{130} of\ the\ 1st\ kind\ I_\nu(x)\\[10](1)\ x^2y''+xy'-(x^2+\nu^2)y=0\\\hspace{25} y=I_\nu(x)\\[10](2)\ I_\nu(x)={\large\sum_{\small k=0}^{\small\infty}\frac{1}{k!\Gamma(k+\nu+1)}(\frac{x}{2})^{\nu+2k}}\\(3)\ {\large e^{\frac{x}{2}(t+{\large\frac{1}{t}})}}={\large\sum_{\small n=-\infty}^{\small\infty}}I_n(x)t^n,\hspace{20} n=integer\\$

Modified Bessel function of the 1st kind (chart)
 [1-10] /10 Disp-Num5103050100200
[1]  2016/02/04 17:26   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Fit a Von Mises distribution in an animal movement study.
from Keisan
Please refer to "von Mises distribution Calculator"
[2]  2015/02/06 05:16   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Help to factorize this Bessel function by its zeros.... ie with positive and negative roots differently
BesselJ(1, sqrt(a^2+s/c)*b)
Comment/Request
Help to factorize this Bessel function by its zeros.... ie with positive and negative roots differently
BesselJ(1, sqrt(a^2+s/c)*b)
[3]  2013/05/29 06:14   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
research in gravitational physics
[4]  2012/08/13 17:02   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
calculation of several bessel functions
Comment/Request
Thanks a lot!
[5]  2012/07/13 05:49   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
To find the amplitude of the output of a one transistor oscillator
[6]  2012/05/17 21:06   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
Testing the accuracy of a routine I wrote
[7]  2012/04/15 10:21   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
To check a routine I wrote for accuracy.
[8]  2011/06/29 20:24   Male / 30 years old level / A student / Very /
Purpose of use
To evaluate a fluid-dynamics related analytic solution.
Comment/Request
It seems to be quite easy to use. Thanks!
[9]  2010/08/21 23:41   - / More than 60 / Self-employed people / Very /
Purpose of use
PHd Thesis
Comment/Request
I would like concise formula for I0, I1 etc
[10]  2010/04/24 07:48   Female / 20 level / A university student / Very /
Purpose of use
Goldstein Factor calcultions. computing bessel functions and their derivatives.
Comment/Request
Wonderful use. almost necessary for my thesis work. should be better publicized for work in mathematics

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