Difference between revisions of "Manuals/calci/BESSELJ"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
<div style="font-size:30px">'''BESSELJ(x,n)'''</div><br/> | <div style="font-size:30px">'''BESSELJ(x,n)'''</div><br/> | ||
| − | * | + | *<math>x</math> is the value to evaluate the function |
| + | *<math>n</math> is the order of the Bessel function and is an integer | ||
==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: 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 α is the | + | where α is the arbitrary complex number. |
*But in most of the cases α is the non-negative real 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 solutions of this equation are called Bessel Functions of order n. | ||
*Bessel functions of the first kind, denoted as Jn(x), and | *Bessel functions of the first kind, denoted as Jn(x), and | ||
| − | *The Bessel function of the first kind of order can be expressed as:Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1), where gamma(n+k+1)=(n+k)! or *Integral 0 to infinity x^(n+k).e^-x dx. is the gamma function. | + | *The Bessel function of the first kind of order can be expressed as: Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1), where gamma(n+k+1)=(n+k)! or *Integral 0 to infinity x^(n+k).e^-x dx. is the gamma function. |
*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 | *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== | ==Examples== | ||
Revision as of 23:17, 1 December 2013
BESSELJ(x,n)
- is the value to evaluate the function
- is the order of the Bessel function and is an integer
is the value to evaluate the function
is the order of the Bessel function and is an integerDescription
- 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 α is the arbitrary 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.
- Bessel functions of the first kind, denoted as Jn(x), and
- The Bessel function of the first kind of order can be expressed as: Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1), where gamma(n+k+1)=(n+k)! or *Integral 0 to infinity x^(n+k).e^-x dx. is the gamma function.
- 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
- BESSELJ(2,3)=0.12894325(EXCEL)Jn(x)=0.10728467204(calci)J1(x)0.5767248079(Actual)J1(x)
- BESSELJ(7,2)=-0.301417224(EXCEL)Jn(x)=NAN(calci)=-0.0046828257(Actual)J1(x)
- BESSELJ(5,1)=-0.327579139(EXCEL)Jn(x)=NAN(calci)