Gibbs%20phenomenon
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31—40 of 111 matching pages
31: Foreword
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►November 20, 2009
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32: 13.30 Tables
33: 28.16 Asymptotic Expansions for Large
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28.16.1
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34: 7.24 Approximations
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Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
35: 25.3 Graphics
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36: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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37: 25.12 Polylogarithms
38: 9.18 Tables
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Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.
39: 6.12 Asymptotic Expansions
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►For re-expansions of the remainder term leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv), with .
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