# A to Z of Excel Functions: the BESSELY Function

14 November 2016

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

**The BESSELY 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. **BESSELY **returns the Bessel function, which is also called the Weber function or the Neumann function.

The **BESSELY **function employs the following syntax to operate:

**BESSELY(x, n)**

The **BESSELY** function has the following arguments:

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

It should be further noted that:

- If
**x**is nonnumeric,**BESSELY**returns the*#VALUE!*error value - If
**n**is nonnumeric,**BESSELY**returns the*#VALUE!*error value - If
**n**< 0,**BESSELY**returns the*#NUM!*error value - The
**n**^{th}order Bessel function of the variable**x**is:

where **J _{v}** is the

**BESSELJ**function and the others are the usual trigonometric functions.

Please see yet another 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.*