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Calculation of the gamma function by Stirling’s formula

Author: Robert Spira
Journal: Math. Comp. 25 (1971), 317-322
MSC: Primary 65D20
MathSciNet review: 0295539
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Abstract: In this paper, we derive a simple error estimate for the Stirling formula and also give numerical coefficients.

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  • N. G. de Bruijn, Asymptotic methods in analysis, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1958. MR 0099564
  • John W. Wrench Jr., Concerning two series for the gamma function, Math. Comp. 22 (1968), 617–626. MR 237078, DOI
  • R. Spira, Table of the Riemann Zeta Function, UMT files, reviewed in Math. Comp., v. 18, 1964, pp. 519-521. Table of the Gamma Function for Complex Arguments, Nat. Bur. Standards, Appl. Math. Series, vol. 34, 1954.
  • E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469
  • N. Nielsen, Die Gammafunction. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten, Chelsea, New York, 1965. MR 32 #2622. R. Spira, Fortran Multiple Precision. Parts I, II, Mathematics Department, Michigan State University, East Lansing, Michigan, 1970.

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Keywords: Asymptotic series, gamma function
Article copyright: © Copyright 1971 American Mathematical Society