Difference between revisions of "Manuals/calci/BESSELY"

Revision as of 04:05, 29 November 2013

BESSELY(x,n)

Where x is the value at which to evaluate the function and n is the integer which is the order of the Bessel function

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: 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^2 (\frac{d^2 y}{dx^2} + x(dy/dx) + (x^2 - α^2)y =0}

where α is the arbitary complex number.

But in most of the cases α 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)=lt p tends to n {Jp(x)Cosp pi()- J-p(x)}/Sinp 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 numeric2. n<0, because n is the order of the function

@@ Line 4: / Line 4: @@
 *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 (d^2 y/dx^2) + x(dy/dx) + (x^2 - α^2)y =0
+*Bessel's Differential Equation is defined as: <math>x^2 (\frac{d^2 y}{dx^2} + x(dy/dx) + (x^2 - α^2)y =0</math>
 where α is the arbitary complex number.
 *But in most of the cases α is the non-negative real number.
@@ Line 11: / Line 11: @@
 *The Bessel function of the 2nd kind of order  can be expressed as: Yn(x)=lt p tends to n {Jp(x)Cosp pi()- J-p(x)}/Sinp 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 numeric2. n<0, because n is the order of the function
 ==Examples==