Manuals/calci/BESSELY

BESSELY(x,n)

• $x$ is the value at which to evaluate the function
• $n$ is the integer which is the order of the Bessel Function
  • BESSELY(), returns the Bessel Function Yn(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 $n$.
• The Bessel function of the second kind $Yn(x)$ and sometimes it is called Weber Function or the Neumann Function..
• The Bessel function of the 2nd kind of order can be expressed as: $Yn(x)=\lim _{p\to n}{\frac {J_{p}(x)Cos(p\pi )-J_{-p}(x)}{Sin(p\pi )}}$
• where $Jn(x)$ is the Bessel functions of the first kind.
• This function will give the result as error when:

1. $x$ or $n$ 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 BESSELY 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 BESSELY(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 at which 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 integer which is the order of the Bessel Function

Examples

1. =BESSELY(2,3) = -1.127783765
2. =BESSELY(0.7,4)= -132.6340573
3. =BESSELY(9,1) = 0.104314575
4. =BESSELY(2,-1) = NAN

Related Videos

BESSEL Equation

See Also

• BESSELI
• BESSELK
• BESSELJ

References

Bessel Function

• List of Main Z Functions

• Z3 home