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31—40 of 57 matching pages
31: 5.17 Barnes’ -Function (Double Gamma Function)
32: Bibliography V
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Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives.
Quart. Appl. Math. 62 (3), pp. 493–507.
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33: 11.11 Asymptotic Expansions of Anger–Weber Functions
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βΊFor sharp error bounds and exponentially-improved extensions, see Nemes (2018).
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βΊThe later references also contain exponentially-improved extensions of (11.11.8) and (11.11.10).
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34: 9.7 Asymptotic Expansions
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§9.7(v) Exponentially-Improved Expansions
…35: 10.74 Methods of Computation
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βΊFurthermore, the attainable accuracy can be increased substantially by use of the exponentially-improved expansions given in §10.17(v), even more so by application of the hyperasymptotic expansions to be found in the references in that subsection.
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36: 13.29 Methods of Computation
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βΊHowever, this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied by the combination of (13.7.10) and (13.7.11), or by use of the hyperasymptotic expansions given in Olde Daalhuis and Olver (1995a).
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37: 19.14 Reduction of General Elliptic Integrals
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βΊIt then improves the classical method by first applying Hermite reduction to (19.2.3) to arrive at integrands without multiple poles and uses implicit full partial-fraction decomposition and implicit root finding to minimize computing with algebraic extensions.
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38: 25.14 Lerch’s Transcendent
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25.14.6
if ;
, if .
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39: 30.16 Methods of Computation
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βΊApproximations to eigenvalues can be improved by using the continued-fraction equations from §30.3(iii) and §30.8; see Bouwkamp (1947) and Meixner and Schäfke (1954, §3.93).
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40: 22.19 Physical Applications
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22.19.6
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