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11: 18.36 Miscellaneous Polynomials

… ►Similar OP’s can also be constructed for the Laguerre polynomials; see Koornwinder (1984b, (4.8)). …

12: 31.8 Solutions via Quadratures

… ►the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows. … ►The solutions in this section are finite-term Liouvillean solutions which can be constructed via Kovacic’s algorithm; see §31.14(ii).

13: 7.20 Mathematical Applications

… ►The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv). …

14: 25.3 Graphics

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15: Philip J. Davis

… ►After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. …

16: 22.8 Addition Theorems

… ►Greenhill (1959, pp. 121–130) reviews these results in terms of the geometric poristic polygon constructions of Poncelet. …

17: 20.11 Generalizations and Analogs

… ►Similar identities can be constructed for ${}_{2}F_1(\frac{1}{3},\frac{2}{3};1;k^2)$, ${}_{2}F_1(\frac{1}{4},\frac{3}{4};1;k^2)$, and ${}_{2}F_1(\frac{1}{6},\frac{5}{6};1;k^2)$. …For applications to rapidly convergent expansions for $\pi$ see Chudnovsky and Chudnovsky (1988), and for applications in the construction of elliptic-hypergeometric series see Rosengren (2004). …

18: Preface

… ►The DLMF has been constructed specifically for effective Web usage and contains features unique to Web presentation. …

19: 4.7 Derivatives and Differential Equations

… ►When $a^z$ is a general power, $\ln a$ is replaced by the branch of $\mathrm{Ln}a$ used in constructing $a^z$. …

20: Bibliography W

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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT 46 (1), pp. 195–202.

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External Links:

ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(iv).

Encodings:

BibTeX

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Elliptic Functions. A Constructive Approach. John Wiley & Sons Ltd., Chichester-New York.

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External Links:

ISBN 0-471-96531-6, MathReview (Glenn Stevens), ZentralBlatt

Referenced by:

§20.11(i), §20.4(i), §20.5(i), §20.5(iii), §20.6, §20.7(iv), §20.9(i), §20.9(ii), §20.9(ii), Ch.20, §22.1, §22.11, §22.12, §22.13(i), §22.16(i), §22.2, §22.20(ii), Figure 22.3.2, Figure 22.3.2, §22.4(i), §22.4(ii), §22.6(i), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), Ch.22, §23.1, §23.10(ii), §23.15(i), §23.17(i), §23.18, §23.2(i), §23.21(ii), §23.3(i), §23.3(ii), §23.5(i), §23.5(ii), §23.5(iii), §23.5(iv), §23.5(v), §23.6(i), §23.8(ii), Ch.23, §4.21(iii), Profile Peter L. Walker.

Encodings:

BibTeX

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