Bessel Function Calculator

Calculate Bessel functions J_n(x) and Y_n(x)

Order (n) - must be non-negative integer

Argument (x)

First Kind

J_n(x) = Σ((-1)^k / (k!(n+k)!)) × (x/2)^(n+2k)

Series expansion

Second Kind

Y_n(x) = Neumann function

Also called Weber function

Recurrence Relation

J_(n-1)(x) + J_(n+1)(x) = (2n/x)J_n(x)

Useful for computation

Differential Equation

x²y'' + xy' + (x² - n²)y = 0

Bessel's equation

Physics

• Wave propagation

• Heat conduction

• Vibrating membranes

Engineering

• Signal processing

• Antenna design

• Acoustic analysis

Mathematics

• Cylindrical coordinates

• Special functions

• Fourier analysis