Manuals/calci/BESSELI
BESSELI(x,n)
- where 'x' is the value at which to evaluate the function and 'n' is the 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 (d^2 y/dx^2) + x(dy/dx) + (x^2 - α^2)y =0
where α is the arbitary 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
- BESSELJ(2,3)=0.12894325(EXCEL)Jn(x)
=0.10728467204(calci)J1(x)
0.5767248079(Actual)J1(x)
- BESSELJ(7,2)=-0.301417224(EXCEL)Jn(x)
=NAN(calci)
=-0.0046828257(Actual)J1(x)
- BESSELJ(5,1)=-0.327579139(EXCEL)Jn(x)
=NAN(calci)