A to Z of Excel Functions: The BESSELK Function

Welcome back to our regular A to Z of Excel Functions blog.  Today we look at the BESSELK function.

The BESSELK function

Bessel functions were first defined by the mathematician Daniel Bernoulli and then generalised by Friedrich Bessel as the canonical solutions y(x) of the differential equation

(known as Bessel's differential equation) for an arbitrary complex number α, the order of the Bessel function.  Although α and −α produce the same differential equation for real α, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α.

This is not meant to be a mathematical lecture.  I will be out of my depth very quickly.  Essentially, Excel has four modified Bessel functions, which may be used by specialists as and when needed.  BESSELK returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.

The BESSELK function employs the following syntax:

The BESSELK function has the following arguments:

• x: required.  This is the value at which to evaluate the function
• n: also required.  This represents the order of the Bessel function.  If n is not an integer, it is truncated accordingly.

It should be further noted that:

• If x is nonnumeric, BESSELK returns the #VALUE! error value
• If n is nonnumeric, BESSELK returns the #VALUE! error value
• If n < 0, BESSELK returns the #NUM! error value
• The n^th order modified Bessel function of the variable x is:

where J_n and Y_n are the J (BESSELJ) and Y (BESSELY) Bessel functions, respectively.

Please see my highly informative example below:

We’ll continue our A to Z of Excel Functions soon.  Keep checking back – there’s a new blog post every other business day.