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.
J. J. Markham, Rev. Mod. Phys. 31, 956 (1959)
T. H. Keil, Phys. Rev. A 140, 601 (1965)
C. S. Kelley, Phys. Rev. B 6, 4112 (1972)
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.
C. S. Kelley, Phys. Rev. B 8, 1806 (1973)
C. S. Kelley, J. Chem. Phys. 68, 1322 (1978)
J. J. Markham, Rev. Mod. Phys. 31, 956 (1959)
T. H. Keil, Phys. Rev. A 140, 601 (1965)
C. S. Kelley, Phys. Rev. B 6, 4112 (1972)
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.
C. S. Kelley, Phys. Rev. B 8, 1806 (1973)
C. S. Kelley, J. Chem. Phys. 68, 1322 (1978)
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Article copyright:
© Copyright 1979
American Mathematical Society