# 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

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

## Related Videos

## See Also

## References