Manuals/calci/BESSELJ

BESSELJ(x,n)

• $x$ is the value to evaluate the function
• $n$ is the order of the Bessel function and is an integer

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:

$Jn(x)=\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{k!\Gamma (n+k+1)}}.({\frac {x}{2}})^{n+2k}$

• where $\Gamma (n+k+1)=(n+k)!$ or
• $\int \limits _{0}^{\infty }x^{n+k}*e^{-x}dx$ is the Gamma Function.
• This function will give result as error when

1. $x$ or $n$ is non numeric
2. $n<0$, because $n$ is the order of the function

Examples

1. BESSELJ(2,3)=0.12894325(EXCEL)Jn(x)=0.10728467204(calci)J1(x)0.5767248079(Actual)J1(x)
2. BESSELJ(7,2)=-0.301417224(EXCEL)Jn(x)=NAN(calci)=-0.0046828257(Actual)J1(x)
3. BESSELJ(5,1)=-0.327579139(EXCEL)Jn(x)=NAN(calci)

See Also

• BESSELI
• BESSELK
• BESSELY

References

Absolute_value