besselY – Science is beautiful

Bessel’s function

2025年4月9日2025年4月9日 by fdtdfem

The detailed proofs of the key properties of Bessel functions of the first kind \( J_n(x) \) and the second kind \( Y_n(x) \). We’ll focus on:ODE derivationSeries expansion derivation for \( J_n(x) \)Parity proofRecurrence relationsDifferentiation identitiesAsymptotic behaviorDefinition and properties of \( Y_n(x) \) Bessel’s Differential EquationWe start from the ODE:\[x^2 y” + x y’ … Read more

Bessel function in Javascript

2025年4月9日 by fdtdfem

Bessel functions are fundamental in many physics and engineering problems described in cylindrical/polar coordinates. While math.js is extensible, it doesn’t include them by default. Here is how to extend it.