BESSELJ in Collabora Office: Evaluate Ordinary First-Kind Bessel Functions

=BESSELJ(X; N)

X is the evaluation point. N is the nonnegative order, with zero explicitly permitted by the condition N ≥ 0 in Collabora help. Both arguments are required; neither has an omitted default.

Collabora’s section explicitly shows that the fractional part of N is ignored: order 4.333 produces the order-four result. This does not provide general fractional-order Bessel evaluation. Negative orders are outside the documented input contract.

The function accepts at least the documented negative-X case =BESSELJ(-1;3), whose stated result is approximately −0.019563353982668. Do not apply a strictly-positive-X rule taken from another Bessel family to BESSELJ.

Enter the numeric input columns below into A2:B7. In C2 enter =BESSELJ(A2;B2) and fill down.

The negative order-zero value at X=3 is a valid mathematical result, not an error indicator. Ordinary Bessel functions can change sign. The rows also show that increasing X need not increase the result: J₀(3) is below J₀(2).

Use a numeric number format with enough decimal places. If only whole numbers are displayed, several distinct values can appear as zero or one even though the underlying results differ.

=BESSELJ(3.45;4)
=BESSELJ(3.45;4.333)

Collabora documents 0.196772639864984 for both. The independently computed J₄(3.45) agrees at that precision. Keep the fraction visible in the input cell when diagnosing accidental order truncation; formatting 4.333 as 4 conceals the cause.

The syntax line in the help uses semicolons, while some displayed examples use commas. This guide uses semicolons consistently. If a formula does not parse in your installation, check its configured argument separator before changing the numeric inputs.

Enter 2 in E2 and 3 in E3. In F2 use =BESSELJ(E2;0) and fill down to F3. The independent outputs are 0.223890779 and −0.260051955. Their opposite signs identify an interval containing a zero of the continuous mathematical J₀ function.

That interval is not the zero itself. A simple midpoint probe at X=2.5 narrows the investigation; calculate =BESSELJ(2.5;0), whose independent value is approximately −0.048383776. The sign change is then between 2 and 2.5.

For a practical root-finding sheet, preserve both endpoints, record the function values, and continue only while the endpoints bracket the desired root. BESSELJ evaluates a function; it does not return a root or select which of many roots your model needs.

The identity J₀(x)+J₂(x)=2J₁(x)/x gives, at X=2:

=BESSELJ(2;0)+BESSELJ(2;2)-BESSELJ(2;1)

The independent residual is zero. The three values are approximately 0.223890779141236, 0.352834028615638, and 0.576724807756873. Use ABS to inspect numerical residual size, and ROUND only when a displayed comparison needs fewer digits.

A sign change, negative output, or value near zero is not by itself a calculation failure. Check that the intended family is J and that N is a nonnegative integer. Do not confuse the order with a requested decimal precision.

The reviewed section does not establish exact native handling of text, empty cells, negative orders, or extreme inputs. Its examples and the independent values here do not certify a native numerical accuracy bound. When using a root in a downstream denominator, test how close it is to zero before division.

The exact function is documented in Collabora Office 26.04 desktop help, retrieved and reviewed on October 17, 2026. This establishes a documentation scope, not the first release that introduced the function or the last version in which it works; those versions and any retirement date remain unestablished. Collabora Online and mobile support are not inferred from desktop help, nor is behavior in another spreadsheet product.

The examples are documentation-based expectations with independent calculations. They have not been executed in Collabora Office. No application screenshot or native error/coercion certification is implied. Formulas use English function names and semicolon argument separators.

• Collabora Office 26.04: BESSELJ (checked October 17, 2026).
• Editorial testing standards.