# Manuals/calci/BESSELK

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BESSELK(x,n)

• Where is the value at which to evaluate the function.
• is the integer which is the order of the Bessel Function.
• Returns the modified Bessel Function Kn(x).

## Description

• This function gives the value of the modified Bessel function when the arguments are purely imaginary.
• 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 Bessel function of the first kind of order can be expressed as:

• The Bessel function of the second kind .
• The Bessel function of the 2nd kind of order can be expressed as:
• So the form of the general solution is .

where: and

are the modified Bessel functions of the first and second kind respectively.

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


## Examples

1. BESSELK(5,2) = 0.005308943735243616
2. BESSELK(0.2,4) = 29900.24920401114
3. BESSELK(10,1) = 0.00001864877394684907
4. BESSELK(2,-1) = #N/A (ORDER OF FUNCTION < 0)

BESSEL Equation