Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Accurate approximations to the polygamma functions


Author: C. Stuart Kelley
Journal: Quart. Appl. Math. 37 (1979), 203-207
MSC: Primary 33A15
DOI: https://doi.org/10.1090/qam/542991
MathSciNet review: 542991
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Abstract: Empirically obtained approximations to the polygamma functions $ {\psi ^{\left( n \right)}}\left( x \right)$ and their associated accuracies are presented. These simple functions are quite accurate, this accuracy increasing with $ x$ and being best for small $ n$. These approximate expressions are shown to be circuitously related to the Stirling approximation to the parent gamma function.


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

  • [1] J. J. Markham, Rev. Mod. Phys. 31, 956 (1959)
  • [2] T. H. Keil, Phys. Rev. A 140, 601 (1965)
  • [3] C. S. Kelley, Phys. Rev. B 6, 4112 (1972)
  • [4] Handbook of mathematical functions, ed. M. Abramowitz and I. A. Stegun, Natl. Bur. Std. (U.S.), Appl. Math. Ser. (U. S. Government Printing Office, Washington, D.C., 1964; Dover, New York, 1965); see especially chapter 6.
  • [5] C. S. Kelley, Phys. Rev. B 8, 1806 (1973)
  • [6] C. S. Kelley, J. Chem. Phys. 68, 1322 (1978)

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DOI: https://doi.org/10.1090/qam/542991
Article copyright: © Copyright 1979 American Mathematical Society


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