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Line 1: − + + + + + + + + + + + + + − <font color="#484848"><font face="Arial, sans-serif"><font size="2">Where 'v' is the value at which to evaluate the function and 'o' is the order of the Bessel function. </font></font></font>+ + + + + − </div>+ − ----+ − <div id="1SpaceContent" class="zcontent" align="left"> <font color="#484848"><font face="Arial, sans-serif"><font size="2">This function returns the Bessel function.</font></font></font></div>+ − ----+ − <div id="7SpaceContent" class="zcontent" align="left"> − * <font color="#484848"><font face="Arial, sans-serif"><font size="2">BESSELJ returns the error value, when 'v' and 'o' are nonnumeric.</font></font></font>+ − * <font color="#484848"><font face="Arial, sans-serif"><font size="2">o should be grater than 1</font></font></font>+ − * <font color="#484848"><font face="Arial, sans-serif"><font size="2">The o-th order Bessel function of the variable 'v' is: </font></font></font> − − <font color="#484848" face="Arial"></font> − − <font color="#484848" face="Arial"></font> − − <font color="#484848" face="Arial"></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">where:</font></font></font> − − <font color="#484848" face="Arial"></font> − − <font color="#484848" face="Arial"></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">is the Gamma function.</font></font></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">where v = x and o = n</font></font></font> − − </div> − ---- − <div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left"> − − BESSELJ − − </div></div> − ---- − <div id="8SpaceContent" class="zcontent" align="left"> <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''BESSELJ(v, o)'''</font></font></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''BESSELJ(C1R1,C2R2)'''</font></font></font> − − <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''<nowiki>=BESSELJ(1.5, 2) is 0.2321</nowiki>'''</font></font></font> − − </div> − ---- − <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div> − ---- − <div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div> − ---- − <div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div> − ---- − <div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div> − ---- − <div id="2SpaceContent" class="zcontent" align="left"> − − {| id="TABLE3" class="SpreadSheet blue" − |- class="even" − | class=" " | − | Column1 − | class=" " | Column2 − | Column3 − | Column4 − |- class="odd" − | class=" " | Row1 − | class="sshl_f" | 1.5 − | class="sshl_f" | 0.232088 − | class="sshl_f" | − | class="sshl_f" | − |- class="even" − | class=" " | Row2 − | class="sshl_f" | 2 − | class="SelectTD SelectTD" | − | − | − |- class="odd" − | Row3 − | class=" sshl_f " | − | − | − | − |- class="even" − | Row4 − | − | − | − | class=" " | − |- class="odd" − | class=" " | Row5 − | − | − | − | − |- class="even" − | Row6 − | − | − | − | − |} − − <div align="left">[[Image:calci1.gif]]</div></div> − ---- − <div id="9SpaceContent" class="zcontent" align="left"><div>[[Image:22.JPG|100%px|http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/22.JPG]]</div></div> − ---- − <div id="13SpaceContent" class="zcontent" align="left"><div>[[Image:21.JPG|100%px|http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/21.JPG]]</div></div> − ----
Manuals/calci/BESSELJ (view source)
Revision as of 06:59, 29 November 2013
, 06:59, 29 November 2013no edit summary
<div id="6SpaceContent" class="zcontent" align="left"> <font color="#484848"><font face="Arial, sans-serif"><font size="2">'''BESSELJ'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">(</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''v'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">, </font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''o'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">)</font></font></font>
<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]