BESSELI Function (LibreOffice Calc)

• Computes Iₙ(x), the modified Bessel function of the first kind
• Supports real values of x
• Supports integer orders n
• Used in heat transfer, wave propagation, diffusion, and statistical distributions

BESSELI(x; n)

Arguments

• x:
  The input value (real number).

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

Compute I₀(x)

=BESSELI(1; 0)
→ 1.266065878

Compute I₁(x)

=BESSELI(2; 1)
→ 1.590636855

Using a cell reference

=BESSELI(A1; B1)

Engineering: cylindrical heat conduction

=BESSELI(R / K; 0)

Probability: Rice distribution component

=BESSELI(A1 * B1; 0)

Differential equation solution (modified Bessel form)

=EXP(-A1) * BESSELI(A1; 0)

Compute a series expansion approximation

=BESSELI(A1; 0) + BESSELI(A1; 1)

Normalize for large x to avoid overflow

=BESSELI(A1; 0) / EXP(A1)

Use with BESSELK for complementary solutions

=BESSELI(A1; 1) + BESSELK(A1; 1)

BESSELI returns a numeric value

Accepts:

• Real x
• Integer n ≥ 0

Behavior details

• Order n must be an integer
• For large x, BESSELI grows exponentially
• For x = 0:
  • I₀(0) = 1
  • Iₙ(0) = 0 for n > 0
• BESSELI is always non‑negative for real x

Invalid input → Err:502

BESSELI of an error → error propagates

• Use BESSELI for modified Bessel solutions in engineering and physics
• Normalize large x values to avoid overflow
• Combine with BESSELK for full solution sets
• Use INT(n) to enforce integer order
• Use EXP and LN for stable transformations

• Use BESSELJ for ordinary Bessel functions
• Use BESSELK for modified Bessel functions of the second kind
• Use BESSELY for Bessel functions of the second kind
• Use EXP, LN, and POWER for analytic transformations

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