Difference between revisions of "Manuals/calci/BESSELJ"
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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''BESSELJ'''</font></font></font><font color="#484...") |
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| − | <div | + | <div style="font-size:30px">'''BESSELJ(x,n)'''</div><br/> |
| + | *where 'x' is the value at which to evaluate the function and n is the integer which is the order of the Bessel function | ||
| + | ==Description== | ||
| + | *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 | ||
| + | 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. | ||
| + | *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== | ||
| − | + | #BESSELI(3,2)=2.245212431(Excel) this is the n th derivative(In(x))=3.9533702171(Calci)this is the 1st derivative(I1(x)) | |
| + | #BESSELI(5,1)=24.33564185 | ||
| + | #BESSELI(6,0)=67.23440724(Excel) I0(x)61.3419369373(CALCI) I1(x) | ||
| + | #BESSELI(-2,1)=0.688948449(Excel) =-1.5906368573(CALCI) | ||
| + | #BESSELI(2,-1)=NAN ,because n<0. | ||
| − | + | ==See Also== | |
| − | + | *[[Manuals/calci/BESSELI | BESSELI ]] | |
| − | + | *[[Manuals/calci/BESSELK | BESSELK ]] | |
| − | + | *[[Manuals/calci/BESSELY | BESSELY ]] | |
| − | |||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Absolute_value| Absolute_value] | |
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Revision as of 01:59, 29 November 2013
BESSELJ(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
Description
- 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
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.
- 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
- BESSELI(3,2)=2.245212431(Excel) this is the n th derivative(In(x))=3.9533702171(Calci)this is the 1st derivative(I1(x))
- BESSELI(5,1)=24.33564185
- BESSELI(6,0)=67.23440724(Excel) I0(x)61.3419369373(CALCI) I1(x)
- BESSELI(-2,1)=0.688948449(Excel) =-1.5906368573(CALCI)
- BESSELI(2,-1)=NAN ,because n<0.