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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On Stieltjes’ continued fraction for the gamma function
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by Bruce W. Char PDF
Math. Comp. 34 (1980), 547-551 Request permission

Abstract:

The first forty-one coefficients of a continued fraction for $\ln \Gamma (z) + z - (z - 1/2) \ln z - \ln \sqrt {2\pi }$ , are given. The computation, based on Wall’s algorithm for converting a function’s power series representation to a continued fraction representation, was run on the algebraic manipulation system MACSYMA.$^{\ast \ast }$
References
    RICHARD FATEMAN, “The MACSYMA ’Big-Floating-Point’ arithmetic system,” Proc. 1976 ACM Sympos. on Symbolic and Algebraic Computation, Assoc. Comput. Mach., New York, 1976, pp. 209-213.
  • Peter Henrici, Applied and computational complex analysis. Vol. 2, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. Special functions—integral transforms—asymptotics—continued fractions. MR 0453984
  • THE MATHLAB GROUP OF THE LABORATORY FOR COMPUTER SCIENCE, MIT, MACSYMA Reference Manual, Version Nine, Massachusetts Institute of Technology, Cambridge, Mass., 1977.
  • Joel Moses, The evolution of algebraic manipulation algorithms, Information processing 74 (Proc. IFIP Congress, Stockholm, 1974) North-Holland, Amsterdam, 1974, pp. 483–488. MR 0411233
  • T. J. STIELTJES, Oeuvres Complètes de Thomas Jan Stieltjes, vol. 2, Noordhoff, Groningen, 1918.
  • H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Co., Inc., New York, N. Y., 1948. MR 0025596
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 547-551
  • MSC: Primary 65A05; Secondary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0559203-3
  • MathSciNet review: 559203