On the computation of values of the psi function from rapidly converging power series expansions
Charles R. Katholi · Journal of Statistical Computation and Simulation · 1978
The computational problem of finding approximate values of a given precision for the Psi or Digamma function is considered. A method based on the approximation from below of an integral representation of the function by a pair of rapidly convergent power series expansions with upper and lower absolute truncation error bounds is derived. The resulting approximation has four free parameters which must be assigned values in any computer program implementing the method. Two possible philosophies for choosing these parameters are discussed and the results of computational trials with two computer codes reflecting these philosophies are given.