Rational approximations for the logarithmic derivative of the gamma function

Abstract

The logarithmic derivative of the gamma function χ(z) can be represented in terms of a generalized hypergeometric function. Using results of our previous studies, we can approximate χ(z) by a sequence of ratios of polynomials. The sequence converges in the half-plane R(z) > 0. Further, numerical computation is facilitated as the numerator and denominator polynomials of the sequence satisfy the same four-term recurrence relation. A similar analysis is developed for χ(z+½)−χ(z). The efficiency of our scheme is illustrated with some numerical examples.

^†This research was supported by the United States Atomic Energy Commission under Contract at(11-1)1619.

^†This research was supported by the United States Atomic Energy Commission under Contract at(11-1)1619.

Notes

^†This research was supported by the United States Atomic Energy Commission under Contract at(11-1)1619.