arbitrary real or complex number &alpha; (the order of the Bessel function ). The most common and important special case is where &alpha; is an integer n . Dividing this equation by x 2 gives: \frac{d^2 f}{dx^2} + \frac{1} {x} \frac{df}{dx} + \left (1 - \frac {\alpha^2} {x^2} \right )f =