GENERATING BESSEL FUNCTIONS WITH AN ANALOG COMPUTER

Because of an indeterminate expression at the origin, Bessel functions J sub n(x) have not been amenable to an accurate generation with analog computers for 0 < x < x max. This report extends an idea of Van Remoortere to use an approximation for 0 < x < x sub 1 and solve a differential equation for x sub 1 < x < x max, combining both phases by switching. The technique described uses Chebyshev polynomials to minimize equipment in the approximation phase, and generates the function 1/x by an integration process in the differential-equation phase to extend the range. The examples given for J sub o, J sub 1, and J sub 9 indicate excellent accuracy for at least 0 < x < 100.