A rapidly convergent series for computing $\psi (z)$ and its derivatives
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- by Peter McCullagh PDF
- Math. Comp. 36 (1981), 247-248 Request permission
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
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M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1970.
Y. L. Luke, The Special Functions and Their Approximations, Academic Press, New York, 1969.
- Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 247-248
- MSC: Primary 65D20; Secondary 33A15
- DOI: https://doi.org/10.1090/S0025-5718-1981-0595057-8
- MathSciNet review: 595057