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.
  • BESSELJ(), returns the modified Bessel Function Jn(x).

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 $J_{n}(x)$
• The Bessel function of the first kind of order can be expressed as:

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

• 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. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
 is non numeric
2. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n < 0}
, because Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
 is the order of the function.

ZOS

• The syntax is to calculate BESSELJ in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BESSELJ(x,n)} .
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the value to evaluate the function
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the order of the Bessel function and is an integer.
• For e.g.,BESSELJ(0.789..0.901..0.025,5)

Examples

1. BESSELJ(2,3) = 0.12894324997562717
2. BESSELJ(7,2) = -0.3014172238218034
3. BESSELJ(5,1) = -0.3275791385663632

Related Videos

BESSEL Equation

See Also

• BESSELI
• BESSELK
• BESSELY

References

Bessel Function

• List of Main Z Functions

• Z3 home