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This article describes the formula syntax and usage of the BESSELK function in Microsoft Excel.


Returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.



The BESSELK function syntax has the following arguments:

  • X    Required. The value at which to evaluate the function.

  • N    Required. The order of the function. If n is not an integer, it is truncated.


  • 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 Jn and Yn are the J and Y Bessel functions, respectively.


Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.




=BESSELK(1.5, 1)

Modified Bessel function at 1.5 with an order of 1.


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