Difference between revisions of "Manuals/calci/BESSELI"
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*The solutions of this equation are called Bessel Functions of order <math>n</math>. | *The solutions of this equation are called Bessel Functions of order <math>n</math>. | ||
*Bessel functions of the first kind, denoted as <math>Jn(x)</math>. | *Bessel functions of the first kind, denoted as <math>Jn(x)</math>. | ||
− | *The <math>n^th</math> order modified Bessel function of the variable <math>x</math> is: <math>In(x)=i^{- | + | *The <math>n^th</math> order modified Bessel function of the variable <math>x</math> is: <math>In(x)=i^{-n}Jn(ix)}</math> ,where <math>Jn(x)=\sum_k=0 \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. | *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. | ||
Revision as of 05:51, 29 November 2013
BESSELI(x,n)
- is the value to evaluate the function
- is an 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:
where 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 .
- Bessel functions of the first kind, denoted as .
- The order modified Bessel function of the variable is: Failed to parse (syntax error): {\displaystyle In(x)=i^{-n}Jn(ix)}} ,where <math>Jn(x)=\sum_k=0 \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
- 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.