BESSELI in Collabora Office: Calculate Modified First-Kind Bessel Values

=BESSELI(X; N)

Both arguments are required. X is the value at which to evaluate the function. N is a nonnegative order, including zero. Although the help calls N a positive integer, its explicit condition is N ≥ 0. Its example with order 4.333 gives the same result as order 4 because the fractional part is ignored.

The documented negative-input example is =BESSELI(-1;3), approximately −0.022168424924332. A negative X therefore is not automatically invalid. This says nothing about negative orders, which are outside the stated contract.

BESSELI computes Iₙ(x), the modified first-kind function. Do not substitute an ordinary first-kind Bessel value Jₙ(x) simply because both names begin with BESSEL. These are different mathematical functions.

Enter the following numeric inputs in A2:B7. In C2 enter =BESSELI(A2;B2) and fill it down through C7. Display nine decimal places.

The order changes the mathematical function, not the number of decimal places displayed. Keep it in its own labeled column. Formatting C2 to zero decimal places does not change the order used in the formula.

These values were independently computed with a high-precision mathematical Bessel implementation. They are targets for a workbook check, not captured Collabora results or a promise of exact final-digit agreement.

The help gives =BESSELI(3.45;4) and =BESSELI(3.45;4.333) with the same documented result, 0.651416873060081. The independent order-four calculation agrees at the shown precision.

This is useful for spotting a model error: entering 4.333 does not request the genuinely fractional-order mathematical function I₄.₃₃₃(x). If your engineering model needs a fractional order, this documented truncation means this function call is not the intended model. Validate the order input as a whole number rather than hiding its fraction with number formatting.

Put X values 1, 2, 3 in E2:E4. Enter =BESSELI(E2;0) in F2 and fill down. In G2 enter =F2/$F$2 and fill down. The expected first ratio is 1; the last is approximately 3.855085799.

This expresses every profile value relative to the value at X=1. It does not make the values probabilities, percentages of a total, or a normalized area. Label the column “ratio to I₀(1)” so a later reader knows exactly what was divided.

For a different profile, verify that the chosen denominator is nonzero before dividing. A convenient reference point is not automatically a valid normalization point for every Bessel family or order.

For a nonzero X, the mathematical identity I₀(x)−I₂(x)=2I₁(x)/x supplies a useful arithmetic check. At X=2, enter:

=BESSELI(2;0)-BESSELI(2;2)-BESSELI(2;1)

The independent residual is zero. The inputs are approximately 2.279585302336067, 0.688948447698738, and 1.590636854637329. In a numerical workbook, inspect a small residual with ABS rather than insisting on exact binary equality.

Keep N nonnegative and use explicit numeric inputs. The dedicated section does not enumerate every text, blank, negative-order, overflow, or coercion error, so this guide does not assign unverified native error codes to those cases.

Large positive arguments can produce very large modified-Bessel values; this guide establishes no safe native maximum. If a result seems too large, first check the family, X, and order, then compare a moderate reference case. ROUND can control presentation, but rounding does not correct an incorrect model or add numerical accuracy.

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