BESSELY in Collabora Office: Evaluate Second-Kind Bessel Functions on Positive Inputs

=BESSELY(X; N)

X is the positive evaluation point. N is the nonnegative order; zero is allowed by the explicit N ≥ 0 condition in Collabora help. Both arguments are required.

The help’s order-4.333 example gives the order-four result because the fractional part is ignored. Therefore, a decimal order does not request general fractional-order Y. Validate N as an integer if users type it into an input cell.

The function computes Yₙ(x), the ordinary second-kind Bessel function. A positive X can produce a positive or negative result. The input domain restriction is not a rule that the output must be positive.

Enter the numeric inputs in A2:B7. In C2 enter =BESSELY(A2;B2) and fill down through C7.

The order-one outputs switch sign between X=2 and X=3. That is mathematical behavior, not an error that should be replaced by zero. Keep signs intact when summing model components; ABS is appropriate only when the question genuinely asks for magnitude.

The expected numbers are independent high-precision calculations rounded for the table. They are not native Collabora observations, and the guide makes no claim that all nine decimals are a guaranteed error bound for every application version.

=BESSELY(3.45;4)
=BESSELY(3.45;4.333)

The vendor gives −0.679848116844476 for both formulas. An independent high-precision order-four calculation is approximately −0.6798481168444754, differing from the documented value in the final shown digit. Both round to −0.679848116844 at twelve decimal places. This comparison does not establish native accuracy. This checks the documented integer-order interpretation, rather than providing a fractional-order calculation.

Do not silently use rounding to change the order. For example, converting 4.8 to 5 before the call asks for a different order than passing 4.8 to a function documented to discard its fractional part.

Put 2 in E2 and 3 in E3. In F2 use =BESSELY(E2;1) and fill down. Independently, the results are approximately −0.107032432 and 0.324674425. A mathematical zero lies between those positive X values because the order-one function is continuous on this interval.

This establishes an interval, not a solved root. For a finer investigation, enter additional positive values inside the interval and retain both the inputs and their signed outputs. A chart can help locate a crossing, but a plotted line or a value displayed as 0.000 is not proof of an exact zero.

If that function value later becomes a denominator, test its magnitude before division. Near a root, a small change in X may cause a large change in a ratio even when the Bessel evaluation itself is behaving normally.

The independent identity Y₀(x)+Y₂(x)=2Y₁(x)/x gives:

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

The mathematical residual is zero. The values are approximately 0.510375672649745, −0.617408104190683, and −0.107032431540938. Keep full stored precision during the subtraction; round only the final display with ROUND if necessary.

This identity is an independent consistency check for the chosen inputs, not certification of the native implementation over its complete domain.

The explicit Collabora error example is =BESSELY(0;3), returning Err:502 because zero is an invalid X. Negative X is also outside the documented strict-positive input domain, but the section does not enumerate every invalid-input error code.

Do not replace X=0 with an arbitrary tiny positive value just to remove an error. The second-kind function has singular behavior near the origin, so that substitution changes the model and can produce a very large magnitude. Text coercion, negative-order handling, extreme precision, and native numerical limits are not established by the reviewed section.

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: BESSELY (checked October 17, 2026).
• Editorial testing standards.