numerical
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11: 35.10 Methods of Computation
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►For small values of the zonal polynomial expansion given by (35.8.1) can be summed numerically.
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►Other methods include numerical quadrature applied to double and multiple integral representations.
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12: Philip J. Davis
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►Davis joined NBS in 1954 when it was becoming the leading center for an emerging field of mathematical research: numerical analysis.
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►In 1957, Davis took over as Chief, Numerical Analysis Section when John Todd and his wife Olga Taussky-Todd, feeling a strong pull toward teaching and research, left to pursue full-time positions at the California Institute of Technology.
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►Davis, easing into his role as Chief, did his part to promote the field of numerical analysis at NBS.
…Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky.
►In 1961, Davis hired Frank W. J. Olver, a founding member of the Mathematics Division and Head of the Numerical Methods Section at the National Physical Laboratory, Teddington, U.
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13: 36.15 Methods of Computation
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►Direct numerical evaluation can be carried out along a contour that runs along the segment of the real -axis containing all real critical points of and is deformed outside this range so as to reach infinity along the asymptotic valleys of .
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►This can be carried out by direct numerical evaluation of canonical integrals along a finite segment of the real axis including all real critical points of , with contributions from the contour outside this range approximated by the first terms of an asymptotic series associated with the endpoints.
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►For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).
14: 9 Airy and Related Functions
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15: 16.25 Methods of Computation
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►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations).
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16: Adri B. Olde Daalhuis
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►Olde Daalhuis has published numerous papers in asymptotics and special functions and in addition to his responsibilities as Mathematics Editor of the DLMF, he is the author or coauthor of the following DLMF Chapters
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17: Karl Dilcher
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►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject.
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18: T. Mark Dunster
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►He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory.
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19: Christopher J. Howls
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►Howls has published numerous papers in the areas of asymptotics and its applications.
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20: Marjorie A. McClain
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► 1956 in Ithaca, New York) is a mathematician in the Applied and Computational Mathematics Division of NIST where she has provided support for mathematical software libraries and assisted with numerical computing projects since 1979.
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