Difference between revisions of "Manuals/calci/BESSELY"

Latest revision as of 07:07, 29 September 2021

BESSELY(x,n)

$x$ is the value at which to evaluate the function
is the integer which is the order of the Bessel Function
- BESSELY(), returns the Bessel Function Yn(x)

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.

The syntax is to calculate BESSELY in ZOS is .
- $x$ is the value at which to evaluate the function
- $n$ is the integer which is the order of the Bessel Function

@@ Line 24: / Line 24: @@
 ==Examples==
-#=BESSELY(2,3) = -1.127783765
+#=BESSELY(2,3) = -1.1277837651220644
-#=BESSELY(0.7,4)= -132.6340573
+#=BESSELY(0.7,4)= -132.6340573047033
-#=BESSELY(9,1) = 0.104314575
+#=BESSELY(9,1) = 0.10431457495919716
 #=BESSELY(2,-1) = #N/A (ORDER OF FUNCTION < 0)