Difference between revisions of "Manuals/calci/BESSELI"
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*This function gives the value of the modified Bessel function. | *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 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: <math>x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> \sum_{n=0}^\infty | + | *Bessel's Differential Equation is defined as: |
| + | <math>x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> \sum_{n=0}^\infty | ||
where <math>\alpha</math> is the arbitrary complex number. | where <math>\alpha</math> is the arbitrary complex number. | ||
*But in most of the cases α is the non-negative real number. | *But in most of the cases α is the non-negative real number. | ||
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where : | where : | ||
<math>Jn(x)=\sum_{k=0}^\infty \frac{(-1)^k}{k!\Gamma(n+k+1)}.(\frac{x}{2})^{n+2k}</math> | <math>Jn(x)=\sum_{k=0}^\infty \frac{(-1)^k}{k!\Gamma(n+k+1)}.(\frac{x}{2})^{n+2k}</math> | ||
| − | *This function will give the result as error when 1.x or n is non | + | *This function will give the result as error when: |
| + | 1.<math>x</math> or <math>n</math> is non numeric | ||
| + | 2.<math>n<0</math>, because <math>n</math> is the order of the function. | ||
==Examples== | ==Examples== | ||
Revision as of 05:15, 29 November 2013
BESSELI(x,n)
- is the value to evaluate the function
- is an integer which is the order of the Bessel function
is the value to evaluate the function
is an integer which is the order of the Bessel functionDescription
- 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:
\sum_{n=0}^\infty where is the arbitrary complex number.
\sum_{n=0}^\infty
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:
.
order modified Bessel function of the variable , where :
,
where :
- This function will give the result as error when:
1. or is non numeric 2., because is the order of the function.
, because Examples
- BESSELI(3,2)=2.245212431(Excel) this is the n th derivative(In(x))=3.9533702171(Calci)this is the 1st derivative(I1(x))
- BESSELI(5,1)=24.33564185
- BESSELI(6,0)=67.23440724(Excel) I0(x)61.3419369373(CALCI) I1(x)
- BESSELI(-2,1)=0.688948449(Excel) =-1.5906368573(CALCI)
- BESSELI(2,-1)=NAN ,because n<0.