BESSELY Function (LibreOffice Calc)
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.
Compatibility
▾| Excel | ✔ |
| Gnumeric | ✔ |
| Google_sheets | ✖ |
| Libreoffice | ✔ |
| Numbers | ✖ |
| Onlyoffice | ✔ |
| Openoffice | ✔ |
| Wps | ✔ |
| Zoho | ✔ |
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.
Related Patterns and Alternatives ▾
- 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.