series
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31—40 of 271 matching pages
31: Frank Garvan
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►His research is in the areas of -series and modular forms, and he enjoys using MAPLE in his research.
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32: Christopher J. Howls
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►In 2008 he was appointed to the editorial board of the Proceedings of the Royal Society of London Series A.
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33: 27.5 Inversion Formulas
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►If a Dirichlet series
generates , and generates , then the product generates
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27.5.6
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27.5.7
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34: 33.23 Methods of Computation
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§33.23(ii) Series Solutions
►The power-series expansions of §§33.6 and 33.19 converge for all finite values of the radii and , respectively, and may be used to compute the regular and irregular solutions. … ►Thus the regular solutions can be computed from the power-series expansions (§§33.6, 33.19) for small values of the radii and then integrated in the direction of increasing values of the radii. … ►Curtis (1964a, §10) describes the use of series, radial integration, and other methods to generate the tables listed in §33.24. … ►Thompson and Barnett (1985, 1986) and Thompson (2004) use combinations of series, continued fractions, and Padé-accelerated asymptotic expansions (§3.11(iv)) for the analytic continuations of Coulomb functions. …35: 8.27 Approximations
36: 11.15 Approximations
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§11.15(i) Expansions in Chebyshev Series
►Luke (1975, pp. 416–421) gives Chebyshev-series expansions for , , , and , , for ; , , , and , , ; the coefficients are to 20D.
MacLeod (1993) gives Chebyshev-series expansions for , , , and , , ; the coefficients are to 20D.
37: 25.8 Sums
38: 24.8 Series Expansions
§24.8 Series Expansions
►§24.8(i) Fourier Series
… ►If and , then … ►§24.8(ii) Other Series
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24.8.9
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