Difference between revisions of "Manuals/calci/BESSELI"

Revision as of 04:46, 29 November 2013

BESSELI(x,n)

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: $x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+(x^{2}-\alpha ^{2})y=0$

where $\alpha$ 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 $Jn(x)$ .
The $n^{t}h$ 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.

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.

@@ Line 6: / Line 6: @@
 *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>
-where <math>\alpha<math> is the arbitrary complex number.
+where <math>\alpha</math> 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.
+*The solutions of this equation are called Bessel Functions of order <math>n</math>.
-*Bessel functions of the first kind, denoted as Jn(x).
+*Bessel functions of the first kind, denoted as <math>Jn(x)</math>.
-*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).
+*The <math>n^th</math> order modified Bessel function of the variable <math>x</math> is: <math>In(x)=i^{-nJn(ix)}</math> ,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.