A rapidly convergent series for computing π(π§) and its derivatives
Peter J McCullagh Β· Mathematics of Computation Β· 1981
We derive a series expansion for Ο ( z ) \psi (z) in which the terms of the expansion are simple rational functions of z . From a computational viewpoint, the new series is of interest in that it converges for all z not necessarily real valued, and is particularly rapid for values of z near the origin. From a mathematical viewpoint the series is of interest in that, although Ο ( z ) \psi (z) has poles at the negative integers and zero, the series is uniformly convergent in any finite interval a > Re β‘ ( z ) > b a > \operatorname {Re} (z) > b .