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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Polynomial type Padé approximants
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by Géza Németh and Magda Zimányi PDF
Math. Comp. 38 (1982), 553-565 Request permission


Some results are established giving conditions on $f(x)$ so that its main diagonal Padé approximation ${R_n}(x)$ is of the form ${P_n}(x)/{P_n}( - x)$, where ${P_n}(x)$ is a polynomial in x of degree n. A number of applications to special functions are presented. Numerical computations are given for the gamma function using the "bignum" arithmetical facilities of formula manipulation languages REDUCE2, FORMAC.
    K. Bahr, "Utilizing the FORMAC novelties," SIGSAM Bull. No. 33, 1975, pp. 21-24.
  • George A. Baker Jr., Essentials of Padé approximants, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0454459
  • A. C. Hearn, REDUCE2 User’s Manual, UCP-19, University of Utah, Salt Lake City, Utah, 1973. Y. L. Luke, The Special Functions and Their Approximations, Vol. 2, Academic Press, New York and London, 1969.
  • Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
  • K. Németh, Padé-Type Approximations (in Hungarian), Unpublished diploma work at Eötvös Loránd University, Budapest, 1980.
  • Oskar Perron, Die Lehre von den Kettenbrüchen. Bd I. Elementare Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1954 (German). 3te Aufl. MR 0064172
  • R. Tobey, J. Baker, R. Crews, P. Marks & K. Victor, PL/I-FORMAC interpreter, 1967.
  • William F. Trench, An algorithm for the inversion of finite Hankel matrices, J. Soc. Indust. Appl. Math. 13 (1965), 1102–1107. MR 189232, DOI 10.1137/0113078
  • John W. Wrench Jr., Concerning two series for the gamma function, Math. Comp. 22 (1968), 617–626. MR 237078, DOI 10.1090/S0025-5718-1968-0237078-4
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 553-565
  • MSC: Primary 41A21; Secondary 33A15, 41A20
  • DOI:
  • MathSciNet review: 645671