Manuals/calci/BESSELI

BESSELI(x,n)

• $x$ is the value to evaluate the function
• $n$ 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: $x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+(x^{2}-\alpha ^{2})y=0$

where <math>\alpha<math> 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

1. BESSELI(3,2)=2.245212431(Excel) this is the n th derivative(In(x))=3.9533702171(Calci)this is the 1st derivative(I1(x))
2. BESSELI(5,1)=24.33564185
3. BESSELI(6,0)=67.23440724(Excel) I0(x)61.3419369373(CALCI) I1(x)
4. BESSELI(-2,1)=0.688948449(Excel) =-1.5906368573(CALCI)
5. BESSELI(2,-1)=NAN ,because n<0.

See Also

• BESSELJ
• BESSELK
• BESSELY

References

| Bessel Function