Difference between revisions of "Manuals/calci/BESSELI"
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<math>I_n(x)=i^{-n}J_n(ix)</math>, | <math>I_n(x)=i^{-n}J_n(ix)</math>, | ||
where : | where : | ||
− | <math>J_n(x)=\sum_{k=0}^\infty \frac{(-1)^k | + | <math>J_n(x)=\sum_{k=0}^\infty \frac{(-1)^k*(\frac{x}{2})^{n+2k} }{k!\Gamma(n+k+1)}</math> |
*This function will give the result as error when: | *This function will give the result as error when: | ||
1.<math>x</math> or <math>n</math> is non numeric | 1.<math>x</math> or <math>n</math> is non numeric |
Revision as of 00:45, 11 December 2013
BESSELI(x,n)
- is the value to evaluate the function
- is an integer which is the order of the Bessel function
Description
- This function gives the value of the modified Bessel function.
- Bessel functions is also called Cylinder Functions because they appear in the solution to Laplace's equation in cylindrical coordinates.
- Bessel's Differential Equation is defined as:
where is the arbitrary complex number.
- But in most of the cases α is the non-negative real number.
- The solutions of this equation are called Bessel Functions of order .
- Bessel functions of the first kind, denoted as .
- The order modified Bessel function of the variable is:
, where :
- This function will give the result as error when:
1. or is non numeric 2., because is the order of the function.
Examples
- BESSELI(3,2) = 2.245212431 this is the derivative of .
- BESSELI(5,1) = 24.33564185
- BESSELI(6,0) = 67.23440724
- BESSELI(-2,1) = 0.688948449
- BESSELI(2,-1) = NAN ,because n<0.