Manuals/calci/BESSELY

BESSELY(x,n)

• Where $x$ is the value at which to evaluate the function
• $n$ 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: $x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+(x^{2}-\alpha ^{2})y=0$

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. $n<0$, because $n$ is the order of the function

Examples

1. BESSELY(2,3)=-1.127783765(EXCEL)Yn(x)=-0.1070324316(CALCI)Y1(x)
2. BESSELY(0.7,4)=-132.6340573(EXCEL)Yn(x)=-1.1032498713(CALCI)Y1(x)
3. BESSELY(9,1)=0.104314575
4. BESSELY(2,-1)=NAN

See Also

• BESSELI
• BESSELK
• BESSELJ

References

Bessel Function