Best rational approximations of entire functions whose Maclaurin series coefficients decrease rapidly and smoothly
Authors:
A. L. Levin and D. S. Lubinsky
Journal:
Trans. Amer. Math. Soc. 293 (1986), 533545
MSC:
Primary 30E10; Secondary 41A20
MathSciNet review:
816308
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Abstract: Let be an entire function which satisfies where and is the positive root of the equation . Let be fixed. Let denote the rational function of type of best approximation to in the uniform norm on . We show that for any sequence of nonnegative integers that satisfies , the rational approximations converge to throughout as . In particular, convergence takes place for the diagonal sequence and for the row sequences of the Walsh array for .
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 D. Braess, On the conjecture of Meinardus on rational approximation to . II, J. Approx. Theory 40 (1984), 375379. MR 740650 (85j:41030)
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 D. S. Lubinsky, Padé tables of a class of entire functions, Proc. Amer. Math. Soc. 94 (1985), 399405. MR 787881 (86i:30045)
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 , Padé tables of entire functions of very slow and smooth growth, Constructive Approx. (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198608163089
PII:
S 00029947(1986)08163089
Keywords:
Padé table,
best rational approximation,
Walsh array
Article copyright:
© Copyright 1986
American Mathematical Society
