Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A rapidly convergent series for computing $ \psi (z)$ and its derivatives


Author: Peter McCullagh
Journal: Math. Comp. 36 (1981), 247-248
MSC: Primary 65D20; Secondary 33A15
MathSciNet review: 595057
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We derive a series expansion for $ \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 $ \psi (z)$ has poles at the negative integers and zero, the series is uniformly convergent in any finite interval $ a < \operatorname{Re} (z) < b$.


References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1970.
  • [2] Y. L. Luke, The Special Functions and Their Approximations, Academic Press, New York, 1969.
  • [3] Yudell L. Luke, Mathematical functions and their approximations, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1975. MR 0501762 (58 #19039)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D20, 33A15

Retrieve articles in all journals with MSC: 65D20, 33A15


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0595057-8
PII: S 0025-5718(1981)0595057-8
Article copyright: © Copyright 1981 American Mathematical Society