Difference between revisions of "Manuals/calci/BESSELY"
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<div style="font-size:30px">'''BESSELY(x,n)'''</div><br/> | <div style="font-size:30px">'''BESSELY(x,n)'''</div><br/> | ||
| − | *Where x is the value at which to evaluate the function | + | *Where <math>x</math> is the value at which to evaluate the function |
| + | *<math>n</math> is the integer which is the order of the Bessel Function | ||
==Description== | ==Description== | ||
*This function gives the value of the modified Bessel function. | *This function gives the value of the modified Bessel function. | ||
| − | *Bessel functions is also called | + | *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: <math>x^2 | + | *Bessel's Differential Equation is defined as: <math>x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> |
| − | where | + | where <math>\alpha</math> is the arbitrary complex number. |
| − | *But in most of the cases | + | *But in most of the cases <math>\alpha</math> is the non-negative real number. |
| − | *The solutions of this equation are called Bessel Functions of order n. | + | *The solutions of this equation are called Bessel Functions of order <math>n</math>. |
| − | *The Bessel function of the second kind | + | *The Bessel function of the second kind <math>Yn(x)</math> 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)= | + | *The Bessel function of the 2nd kind of order can be expressed as: <math>Yn(x)= \lim_{p \to \n}\frac{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 | *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 | ||
Revision as of 22:46, 1 December 2013
BESSELY(x,n)
- Where is the value at which to evaluate the function
- is the integer which is the order of the Bessel Function
is the value at which to evaluate the function
is the integer which is the order of the Bessel FunctionDescription
- 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:
where is the arbitrary complex number.
is the arbitrary complex number.
- But in most of the cases is the non-negative real number.
- The solutions of this equation are called Bessel Functions of order .
- The Bessel function of the second kind and sometimes it is called Weber Function or the Neumann Function..
- The Bessel function of the 2nd kind of order can be expressed as: <math>Yn(x)= \lim_{p \to \n}\frac{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
and sometimes it is called Weber Function or the Neumann Function..Examples
- BESSELY(2,3)=-1.127783765(EXCEL)Yn(x)=-0.1070324316(CALCI)Y1(x)
- BESSELY(0.7,4)=-132.6340573(EXCEL)Yn(x)=-1.1032498713(CALCI)Y1(x)
- BESSELY(9,1)=0.104314575
- BESSELY(2,-1)=NAN