Difference between revisions of "Manuals/calci/BESSELI"

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<math>I_n(x)=i^{-n}J_n(ix)</math>,  
 
<math>I_n(x)=i^{-n}J_n(ix)</math>,  
 
where :
 
where :
<math>J_n(x)=\sum_{k=0}^\infty \frac{(-1)^k}{k!\Gamma(n+k+1)}.(\frac{x}{2})^{n+2k}</math>
+
<math>J_n(x)=\sum_{k=0}^\infty \frac{(-1)^k*(\frac{x}{2})^{n+2k} }{k!\Gamma(n+k+1)}</math>
 
*This function will give the result as error when:
 
*This function will give the result as error when:
 
  1.<math>x</math> or <math>n</math> is non numeric
 
  1.<math>x</math> or <math>n</math> is non numeric

Revision as of 00:45, 11 December 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:

, where :

  • This function will give the result as error when:
1. or  is non numeric
2., because  is the order of the function.

Examples

  1. BESSELI(3,2) = 2.245212431 this is the derivative of .
  2. BESSELI(5,1) = 24.33564185
  3. BESSELI(6,0) = 67.23440724
  4. BESSELI(-2,1) = 0.688948449
  5. BESSELI(2,-1) = NAN ,because n<0.

See Also

References

Bessel Function