Zoho Sheet BESSELY Function: Orders, Controls and Numerical Checks

Zoho’s official BESSELY entry was retrieved on October 15, 2026. The entry documents the rolling web service; it does not establish the first introduction release or last functioning version. Both historical endpoints are unknown, and mobile/offline parity is unverified. The calculated expectations here are independent reference values, not captured native Zoho results.

BESSELY(x; n)

Both arguments are required. x is the evaluation point and n is the order. Zoho’s argument description asks for n greater than zero, while its error list specifically names n below zero. The zero-order boundary is therefore not fully resolved by this reference. Use positive integer orders in this guide; no truncation rule for arbitrary fractional n is assumed.

Zoho also asks for x greater than zero. Its error list names negative x, leaving the exact native zero-input error unspecified. All working examples below keep x strictly positive. A mathematical continuation to other arguments is not evidence that this worksheet function supports it.

These are the vendor’s explicit argument pairs, evaluated independently. Some final displayed digits differ slightly from the help’s approximations; the table gives the independent values rather than treating the vendor’s last digit as an exact numerical contract. More displayed digits here do not certify Zoho’s accuracy over every input range.

Create BesselValues with x in A1, Order in B1 and Result in C1. Enter the six rows below and fill C2 =BESSELY(A2;B2) through C7. The table changes x and n explicitly; do not confuse an increase in order with an increase in the evaluation point.

In a copy change A4 from 2 to 2.5, leaving B4 equal to 1. C4 becomes approximately 0.145918138. The other rows do not change. Display at least nine decimal places for these controls; a coarse number format can hide a meaningful difference.

At x=2 and central order n=2, evaluate orders 1,2,3. The ordinary recurrence adds the neighboring orders. Use this direct formula:

=BESSELY(2;1)+BESSELY(2;3)-2*BESSELY(2;2)

The mathematical residual is zero, from F₁(2)+F₃(2)=2F₂(2). In a spreadsheet, inspect a small numerical residual rather than demanding exact floating-point equality. The identity is supported by the NIST recurrence reference; it does not verify Zoho’s implementation or establish a universal tolerance.

For order 1, =BESSELY(2;1) is approximately -0.107032432, while =BESSELY(3;1) is approximately 0.324674425. The opposite signs bracket at least one zero of the continuous mathematical function on this positive interval. The midpoint 2.5 gives approximately 0.145918138.

A sign-change check is a starting point for a documented root-finding method, not an exact root or a guarantee of uniqueness. Keep the order fixed as x changes. Do not divide by the function value near a zero when normalizing a model, since a small denominator can magnify error. No native Goal Seek or Solver calculation was performed.

Zoho documents #NUM! for negative n, and for negative x. The zero-order ambiguity noted above is kept separate from those explicit error rules. The shared glossary also mentions invalid type, name and reference errors without specifying all blank, text or array coercions.

If the sign, magnitude or scale seems wrong, check x versus n, the selected family, and whether a displayed zero is only rounding. Oscillating values can cross zero as x changes; a negative result is not automatically an error. Mathematical reference calculations do not establish platform parity or a guaranteed number of significant digits in Zoho.