Manuals/calci/BESSELJ
BESSELJ(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), and
- The Bessel function of the first kind of order can be expressed as:Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1), where gamma(n+k+1)=(n+k)! or *Integral 0 to infinity x^(n+k).e^-x dx. is the gamma function.
- This function will give the result as error when 1.x or n is non numeric 2. 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)