BESSELI in WPS Spreadsheet: Modified Bessel I Values

=BESSELI(x,n)

Both arguments are required. x is the numeric argument and n is the order. Supply the order explicitly; it is not an optional precision setting. The lesson says noninteger orders are truncated, but the reproducible examples below use positive integers, avoiding dependence on truncation and borderline inputs.

Use positive x for this worked table. It is a deliberately small domain for comparing the documented kernel, not a certification of extreme-argument accuracy or all real inputs. A Bessel value is a real numeric result here, not complex text.

1. In a fresh sheet, put x, Order and Result in A1:C1.
2. Enter the numeric x and order values below in columns A and B.
3. Enter =BESSELI(A2,B2) in C2. Copy it down through C5, keeping both references relative.
4. Compare the results with these independently calculated reference values; round only for display.

Rows 2 and 3 hold the order fixed while changing x. Rows 2 and 4 hold x fixed while changing the order. This separates two effects that would be mixed together if every input changed at once. The first row also agrees mathematically with the literal formula in the quick answer.

Unlike the alternating J series, its terms are positive for the positive arguments used here. At order 1, increasing x from 1 to 2 increases the value from 0.5651591040 to 1.5906368546. This is not a probability and is not bounded above by 1.

The identity printed in the lesson relates Iₙ(x) to Jₙ(ix) with a complex phase factor. That does not mean entering complex text into BESSELI: its documented x argument is numeric. The WPS 2019 walkthrough instead uses ordinary numeric x = 2.5 and order 2, displaying approximately 1.276466159. Independent evaluation of I₂(2.5) gives approximately 1.276466147819, so the historical display should not be used as a high-precision reference.

Compare the two orders at each x. At x = 1, I₂/I₁ is approximately 0.2401937239; at x = 2 it is approximately 0.4331274267. These ratios normalize one mathematical curve against another, rather than converting either curve into a probability.

Keep the original x and order beside every result. A chart of just the output column loses the distinction between changing the argument and changing the order. If you build a larger grid, use one row per x and one column per order, then check several individual cells against explicit literal formulas before interpreting a trend.

The official lesson documents #VALUE! for a nonnumeric x or order, and #NUM! for a negative order. Thus =BESSELI("bad",1) and =BESSELI(1,-1) are documentation-based error expectations, not executed error captures.

The examples do not establish how numeric-looking text, blank cells, logical values or existing spreadsheet errors are coerced. Do not infer the error returned at zero or negative x from another spreadsheet program.

Use a function because its mathematical definition matches the intended calculation, not merely because its name contains “Bessel.” These four names describe different kernels, not legacy aliases. The lesson alone provides no broad precision, overflow, underflow or large-order guarantee.

The official WPS Academy BESSELI lesson, published 2019-05-05, was rechecked on October 19, 2026. The lesson explicitly labels WPS Office for Windows Personal. Its narrative explicitly names WPS 2019 as the tutorial context. The publication date is evidence that the function was documented by that date, not its introduction date. Exact numeric builds, first and last supported versions remain unknown. The lesson does not establish retirement or deprecation, or parity across platforms and editions.

These are original documentation-based examples with independently calculated expected values. They were not executed in WPS. Vendor demonstrations are historical documentation, not our application tests. Display rounding, client precision and workbook interchange remain unverified; the extra digits in this guide are mathematical reference values. English function names and comma separators follow the lesson.

• BESSELJ: compare the distinct mathematical kernel.
• BESSELK: compare the distinct mathematical kernel.
• BESSELY: compare the distinct mathematical kernel.