## ABSTRACT

The computation of mathematical functions is a part of the scientific computing infrastructure that has not benifited very much from parallel and vector hardware. Special functions are needed in many scientific and engineering calculations but the availability of good software, even for serial computers, is limited. The approaches used heretofore include power series, asymptotic series, and recurrence relations. To these we add the defining differential equation which we integrate in parallel. Our method and its implementation in Fortran Software for the Bessel function J_{n}
when n is an integer will be described. The program has been tested on a parallel computing cluster of DEC Alpha CPUs under Parallel Virtual Machine (PVM) environment. Accuracy and speedup due to parallelism will be discussed.