Difference between revisions of "Manuals/calci/BESSELI"
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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">'''BESSELI'''</font></font></font><font color="#484...") |
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| − | <div | + | <div style="font-size:30px">'''BESSELI(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). | ||
| + | *The n-th order modified Bessel function of the variable x is: In(x)=i^-nJn(ix) ,where Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1). | ||
| + | *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== | ||
| − | + | #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) | ||
| − | + | ==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 01:19, 29 November 2013
BESSELI(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).
- The n-th order modified Bessel function of the variable x is: In(x)=i^-nJn(ix) ,where Jn(x)=summation(k=0 to infinity){(-1)^k(x/2)^n+2k}/k!gamma(n+k+1).
- 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
- 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)