Difference between revisions of "Manuals/calci/BESSELJ"
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*Bessel functions is also called Cylinder Functions because they appear in the solution to Laplace's equation in cylindrical coordinates. | *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\frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> | *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 n. | ||
| − | *Bessel functions of the first kind, denoted as Jn(x) | + | *Bessel functions of the first kind, denoted as <math>Jn(x)</math> |
| − | *The Bessel function of the first kind of order | + | *The Bessel function of the first kind of order can be expressed as: <math>Jn(x)=\sum_{k=0}^\infity){(-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 23:19, 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 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 n.
- Bessel functions of the first kind, denoted as
- The Bessel function of the first kind of order can be expressed as: <math>Jn(x)=\sum_{k=0}^\infity){(-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)