Polynomial type Padé approximants
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 by Géza Németh and Magda Zimányi PDF
 Math. Comp. 38 (1982), 553565 Request permission
Abstract:
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.References

K. Bahr, "Utilizing the FORMAC novelties," SIGSAM Bull. No. 33, 1975, pp. 2124.
 George A. Baker Jr., Essentials of Padé approximants, Academic Press [Harcourt Brace Jovanovich, Publishers], New YorkLondon, 1975. MR 0454459 A. C. Hearn, REDUCE2 User’s Manual, UCP19, 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 YorkLondon, 1975. MR 0501762 K. Németh, PadéType Approximations (in Hungarian), Unpublished diploma work at Eötvös Loránd University, Budapest, 1980.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/IFORMAC 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/S00255718196802370784
Additional Information
 © Copyright 1982 American Mathematical Society
 Journal: Math. Comp. 38 (1982), 553565
 MSC: Primary 41A21; Secondary 33A15, 41A20
 DOI: https://doi.org/10.1090/S00255718198206456717
 MathSciNet review: 645671