# Documentation/Calc Functions/BESSELJ

BESSELJ

## Summary:

Calculates the value of a Bessel function of the first kind, usually referred to as Jn(x). n is the order of the function and x is the value at which the function is to be calculated.

BESSELJ(X; N)

## Returns:

Returns a real number which is the value of the Bessel function of the first kind, with a specified order, for a given value of x.

## Arguments:

X is a real number, or a reference to a cell containing that number, which is the value at which the Bessel function of the first kind is to be calculated.

N is a non-negative integer, or a reference to a cell containing that number, which is the order of the Bessel function of the first kind.

• If either X or N is non-numeric, then BESSELJ reports a #VALUE! error.
• If N is a non-integer value, then BESSELJ truncates it to an integer.
• If N is negative, then BESSELJ reports an invalid argument error (Err:502).

### Details specific to BESSELJ function

The following figure shows a plot of the Bessel functions of the first kind for orders 0, 1, 2, and 3.

Bessel functions of the first kind are finite at the origin, x = 0. They exhibit odd or even parity depending on the order of the function, so that Jn(-x) = Jn(x) for even orders and Jn(-x) = -Jn(x) for odd orders.

ODF 1.2 indicates that the first argument to the BESSELJ function should be an integer. However, this is considered an unnecessary limitation and Calc’s implementation caters for real values of X.

### General information about Calc's Bessel functions

 For convenience, the information in this subsection is repeated on all pages describing Calc’s Bessel and modified Bessel functions.

Calc provides two Bessel functions that are solutions of Bessel's differential equation and two modified Bessel functions that are solutions of the modified Bessel equation. The mathematics behind these equations and functions is beyond the scope of this wiki but more information can be found at Wikipedia’s Bessel function page and in the sources that it references.

The four functions provided by Calc are as follows:

• BESSELJ – calculates values of Jn(x), a Bessel function of the first kind, for non-negative integer vales of n.
• BESSELY – calculates values of Yn(x), a Bessel function of the second kind, for non-negative integer vales of n and positive values of x.
• BESSELI – calculates values of In(x), a modified Bessel function of the first kind, for non-negative integer vales of n.
• BESSELK - calculates values of Kn(x), a modified Bessel function of the second kind, for non-negative integer vales of n and positive values of x.

In each case the parameter n is known as the order of the function.

## Examples:

Formula Description Returns
=BESSELJ(3.45; 4) Here the function calculates the value of the Bessel function of the first kind, with order 4, at an x value of 3.45. 0.196772639864984
=BESSELJ(3.45; 4.333) Here the function calculates the value of the Bessel function of the first kind, with order 4.333, at an x value of 3.45. The result is the same as in the previous example, showing that Calc truncates the value of 4.333 to 4. 0.196772639864984
=BESSELJ(-3.45; 4) Here the function calculates the value of the Bessel function of the first kind, with order 4, at an x value of -3.45. The result is the same as in the previous examples, showing that for an even order, the function is even. 0.196772639864984
=BESSELJ(H1; H2) where cells H1 and H2 contain the values 2.6 and 3 respectively. Here the function calculates the value of the Bessel function of the first kind, with order 3, at an x value of 2.6. 0.235293813048964

BESSELJ