Manuals/calci/BESSELJ

BESSELJ(x,n)

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 $\alpha$ is the Arbitrary Complex Number.

But in most of the cases $\alpha$ 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 Bessel function of the first kind of order can be expressed as: Failed to parse (unknown function "\infity"): {\displaystyle Jn(x)=\sum_{k=0}^\infity){(-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

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)