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BESSELK Function

Excel 2007+

Summary

The BESSELK function computes the modified Bessel function of the second kind, useful in engineering applications like heat transfer, vibration analysis, and wave propagation problems. It evaluates Bessel functions for purely imaginary arguments.

Syntax

BESSELK(X, N)

Parameters

Parameter	Type	Required	Description
X	`Number`	Yes	Numeric value at which to evaluate the Bessel function
N	`Number`	Yes	Order of the function (non-negative number, truncated if non-integer)

Using the BESSELK Function

BESSELK is primarily used in technical fields requiring solutions to differential equations involving cylindrical or spherical symmetry. Common applications include thermal conduction in pipes, pressure vessel design, and electromagnetic field analysis.

Common BESSELK Examples

Basic BESSELK Calculation

=BESSELK(1.5, 1)

Returns 0.277387804, the modified Bessel function value at x=1.5 for order 1. Matches official Microsoft example.

Higher Order Example

=BESSELK(2, 2)

Calculates modified Bessel function at x=2 for order 2, useful in vibration analysis.

Engineering Application

=BESSELK(A1, 0)

Uses cell A1 as input value with zero order, common in heat conduction problems.

Frequently Asked Questions

BESSELK returns #NUM! error if the order N is less than zero.

Yes, non-integer orders are truncated to the nearest integer before calculation.

BESSELK computes modified Bessel functions (for imaginary arguments), while BESSELY computes Bessel functions of the second kind.

Common Errors and Solutions

#VALUE!

Cause: X or N argument is non-numeric

Solution: Ensure both arguments contain valid numbers

#NUM!

Cause: N is negative

Solution: Use a non-negative value for the order parameter

#NAME?

Cause: Function name misspelled

Solution: Use exact spelling: BESSELK

Notes

BESSELK corresponds to K_n(x) in mathematical notation
Returns the modified Bessel function: K_n(x) = (π/2) * (I_{-n}(x) - I_n(x)) / sin(nπ)
Most useful when x > 0 and n ≥ 0
Excel truncates non-integer n values automatically

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003, Excel XP, Excel 2000, Excel 97

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+