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Mathematics of Computation

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On Stieltjes' continued fraction for the gamma function

Author: Bruce W. Char
Journal: Math. Comp. 34 (1980), 547-551
MSC: Primary 65A05; Secondary 65D20
MathSciNet review: 559203
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Abstract: The first forty-one coefficients of a continued fraction for $ \ln \;\Gamma (z) + z - (z - {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}})\;\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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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
  • [3] THE MATHLAB GROUP OF THE LABORATORY FOR COMPUTER SCIENCE, MIT, MACSYMA Reference Manual, Version Nine, Massachusetts Institute of Technology, Cambridge, Mass., 1977.
  • [4] 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
  • [5] T. J. STIELTJES, Oeuvres Complètes de Thomas Jan Stieltjes, vol. 2, Noordhoff, Groningen, 1918.
  • [6] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948. MR 0025596

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Keywords: Gamma function, continued fraction, symbolic computation, approximation
Article copyright: © Copyright 1980 American Mathematical Society