Manuals/calci/BESSELI

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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

  1. BESSELI(3,2)=2.245212431(Excel) this is the n th derivative(In(x))=3.9533702171(Calci)this is the 1st derivative(I1(x))
  2. BESSELI(5,1)=24.33564185
  3. BESSELI(6,0)=67.23440724(Excel) I0(x)61.3419369373(CALCI) I1(x)
  4. BESSELI(-2,1)=0.688948449(Excel) =-1.5906368573(CALCI)
  5. BESSELI(2,-1)=NAN ,because n<0.

See Also

References

| Bessel Function