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> | + | *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> |
where α is the arbitrary complex number. | where α 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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*The n-th order modified Bessel function of the variable x is: In(x)=i^-nJn(ix) ,where Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1). | *The n-th order modified Bessel function of the variable x is: In(x)=i^-nJn(ix) ,where Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1). | ||
*This function will give the result as error when 1.x or n is non numeric2. n<0, because n is the order of the function. | *This function will give the result as error when 1.x or n is non numeric2. n<0, because n is the order of the function. | ||
| + | |||
==Examples== | ==Examples== | ||
Revision as of 04:42, 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:
where α 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 n.
- Bessel functions of the first kind, denoted as Jn(x).
- The n-th order modified Bessel function of the variable x is: In(x)=i^-nJn(ix) ,where Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1).
- This function will give the result as error when 1.x or n is non numeric2. n<0, because n is the order of the function.
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.