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BESSELY Function (LibreOffice Calc)

Mathematical Advanced LibreOffice Calc Introduction not established

The BESSELY function returns the Bessel function of the second kind, Yₙ(x). It is used in engineering, physics, acoustics, electromagnetics, and differential equation modeling involving cylindrical or spherical symmetry.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: Documented by LibreOffice 26.8.1.1; original introduction not established.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **BESSELY** function returns the **Bessel function of the second kind**, denoted Yₙ(x). This function appears in engineering, physics, acoustics, electromagnetics, and solutions to differential equations involving cylindrical or spherical symmetry.

What the BESSELY Function Does

  • Computes Yₙ(x), the Bessel function of the second kind
  • Supports real values of x > 0
  • Supports integer orders n
  • Used in wave propagation, acoustics, EM fields, and boundary‑value problems

Syntax

BESSELY(x; n)

Arguments

  • x:
    The input value (real number > 0).

  • n:
    The order of the Bessel function (integer ≥ 0).

Basic Examples

Compute Y₀(x)

=BESSELY(1; 0)
→ 0.088256964

Compute Y₁(x)

=BESSELY(2; 1)
→ 0.107032431

Using a cell reference

=BESSELY(A1; B1)

Advanced Examples

Acoustic wave propagation

=BESSELY(k * r; 0)

Electromagnetic cylindrical wave model

=BESSELY(A1 * B1; 1)

Combine with BESSELJ for general Bessel equation solutions

=C1 * BESSELJ(A1; 0) + C2 * BESSELY(A1; 0)

Solve radial differential equations

=BESSELY(A1; 1) + A1 * BESSELY(A1; 0)

Normalize oscillatory behavior

=BESSELY(A1; 0) / SQRT(A1)

Use in scattering problems

=BESSELY(k * r; n)

Edge Cases and Behavior Details

BESSELY returns a numeric value

Accepts:

  • Real x > 0
  • Integer n ≥ 0

Behavior details

  • Order n must be an integer
  • Yₙ(x) has a singularity at x = 0 (→ –∞)
  • Yₙ(x) oscillates like a sine wave with decreasing amplitude
  • Yₙ(x) → 0 as x → ∞
  • Y₀(x) is undefined at x = 0

Invalid input → Err:502

BESSELY of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • x ≤ 0
  • n is not an integer
  • Non-numeric input

Fix:

  • Ensure x > 0
  • Wrap n with INT()
  • Validate numeric input

Unexpected oscillatory behavior

Cause:

  • Bessel Y functions oscillate naturally
  • Amplitude decreases slowly

Fix:

  • Normalize using SQRT(x)
  • Scale results for stability

Best Practices

  • Use BESSELY for wave, vibration, and cylindrical boundary‑value problems
  • Combine with BESSELJ for complete Bessel equation solutions
  • Normalize large x values for stability
  • Use INT(n) to enforce integer order
  • Pair with EXP, LN, and POWER for analytic transformations
BESSELY is essential for modeling acoustics, EM waves, scattering, and any system governed by ordinary Bessel differential equations.
  • Use BESSELJ for first‑kind Bessel functions
  • Use BESSELI and BESSELK for modified Bessel functions
  • Use EXP, LN, and POWER for analytic transformations

By mastering BESSELY and its companion functions, you can build powerful engineering, physics, and mathematical models in LibreOffice Calc.