Bessel function

Family of solutions to related differential equations

Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena with circular or cylindrical symmetry. They are named after the German astronomer and mathematician Friedrich Bessel, who studied them systematically in 1824. Bessel functions are solutions to a particular type of ordinary differential equation: x 2 d 2 y d x 2 + x d y d x + ( x 2 − α 2) y = 0 , {\displaystyle x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+\left(x^{2}-\alpha ^{2}\right)y=0,} where α {\displaystyle \alpha } is a number that determines the shape of the solution.

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