Chebyshev approximations for the psi function

Authors:
W. J. Cody, Anthony J. Strecok and Henry C. Thacher

Journal:
Math. Comp. **27** (1973), 123-127

MSC:
Primary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1973-0326986-3

MathSciNet review:
0326986

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Abstract | References | Similar Articles | Additional Information

Abstract: Rational Chebyshev approximations to the psi (digamma) function are presented for , and . Maximum relative errors range down to the order of .

**[1]**W. J. Cody, "A survey of practical rational and polynomial approximation of functions,"*SIAM Rev.*, v. 12, 1970, pp. 400-423. MR**42**#2627. MR**0267725 (42:2627)****[2]**P. J. Davis, "Gamma function and related functions," Chapter 6,*Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables*, Edited by M. Abramowitz and I. A. Stegun, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964; 3rd printing, with corrections, 1965. MR**29**#4919; MR**31**#1400. MR**0177136 (31:1400)****[3]**Y. L. Luke,*The Special Functions and Their Approximations*. Vols. 1, 2, Math. in Sci. and Engineering, vol. 53, Academic Press, New York, 1969. MR**39**#3039; MR**40**#2909.**[4]**Y. L. Luke, "Rational approximations for the logarithmic derivative of the gamma function,"*Applicable Anal.*, v. 1, 1971, no. 1, pp. 65-73. MR**43**#5686. MR**0279965 (43:5686)****[5]**J. W. Wrench, Jr., "Concerning two series for the gamma function,"*Math. Comp.*, v. 22, 1968, pp. 617-626. MR**38**#5371. MR**0237078 (38:5371)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0326986-3

Keywords:
Psi function,
digamma function,
rational Chebyshev approximation

Article copyright:
© Copyright 1973
American Mathematical Society