How to Use Excel's BESSELI Function

Excel's BESSELI function stands for "Bessel Imaginary" because it returns the solution to a modified Bessel function of the first kind for a purely imaginary number. Bessel functions have a variety of real-world applications, especially in electromagnetism and heat conduction. The following steps will show how to use Excel's BESSELI function.

Instructions

Difficulty: Moderate

1. Install the Analysis ToolPak if BESSELI returns the #NAME? error value. Select the Add-Ins menu item from the Tools menu, check the box next to the Analysis ToolPak and click on the OK button to install the Analysis ToolPak.
2. Learn the syntax for BESSELI. It's BESSELI(x,n) where x is the value for which the Bessel function will be evaluated and n is the order of the Bessel function. N will be truncated to an integer, if necessary.
3. Interpret the error values returned by BESSELI. A return error value of #VALUE! means that one of the arguments is nonnumeric. BESSELI will return the #NUM! error value if the order < 0.
4. Look at how the nth order BESSEL function is evaluated for purely imaginary numbers. It is: I(x)=(i)^(-n)J(ix) where I(x) is a linearly independent solution to the modified Bessel function of order n, i is the square root of -1 and J(ix) is the unmodified Bessel function for ix of order n. The unmodified Bessel function J(ix) for the order n is the integral of cos(nT-ixsinT)dT/pi over the interval 0 to pi where T is the gamma function.
5. Study this example of BESSELI: =BESSELI(1.5,1) will return 0.981666. This is the value of the first order Bessel function for 1.5i. Note that this modified Bessel function is actually evaluated for xi and not x.

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