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21—30 of 167 matching pages

21: Bibliography S

… ►

T. C. Scott, G. Fee, J. Grotendorst, and W. Z. Zhang (2014) Numerics of the generalized Lambert

W

function. ACM Commun. Comput. Algebra 48 (2), pp. 42–56.

ⓘ

External Links:: FullText, Document, MathReview Entry, ZentralBlatt
Referenced by:: §4.13, §4.13.
Encodings:: BibTeX

… ►

R. Shail (1980) On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

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External Links:: ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt
Referenced by:: §29.17(i), §29.8.
Encodings:: BibTeX

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N. T. Shawagfeh (1992) The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.

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External Links:: ISSN 0253-424X, MathReview
Referenced by:: §9.10(v).
Encodings:: BibTeX

… ►

A. Sidi (2010) A simple approach to asymptotic expansions for Fourier integrals of singular functions. Appl. Math. Comput. 216 (11), pp. 3378–3385.

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External Links:: ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt
Referenced by:: §2.3(iv).
Encodings:: BibTeX

… ►

R. Sips (1965) Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

ⓘ

External Links:: ZentralBlatt
Referenced by:: §28.8(ii).
Encodings:: BibTeX

…

22: 18.36 Miscellaneous Polynomials

… ►Two representative examples, type I

X_{1}

-Laguerre, Gómez-Ullate et al. (2010), and type III

X_{2}

-Hermite, Gómez-Ullate and Milson (2014) EOP’s, are illustrated here. … ►Completeness and orthogonality follow from the self-adjointness of the corresponding Schrödinger operator, Gómez-Ullate and Milson (2014), Marquette and Quesne (2013).

23: 15.12 Asymptotic Approximations

… ►For more details see Farid Khwaja and Olde Daalhuis (2014). …

24: 16.11 Asymptotic Expansions

… ►Explicit representations for the coefficients

c_{k}

are given in Volkmer and Wood (2014). …

25: Bibliography R

… ►

J. T. Ratnanather, J. H. Kim, S. Zhang, A. M. J. Davis, and S. K. Lucas (2014) Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.

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External Links:: ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt
Referenced by:: §10.74(vii), §10.74(vii), 7th item, §10.77(ix).
Encodings:: BibTeX

…

26: 9.9 Zeros

… ►For the distribution in

\mathbb{C}

of the zeros of

\operatorname{Ai}'\left(z\right)-\sigma\operatorname{Ai}\left(z\right)

, where

\sigma

is an arbitrary complex constant, see Muraveĭ (1976) and Gil and Segura (2014). …

27: 18.39 Applications in the Physical Sciences

… ►

p

here being the order of the Laguerre polynomial,

L^{(2l+1)}_{p}

of Table 18.8.1, line 11, and

l

the angular momentum quantum number, and where … ►thus recapitulating, for

Z=1

, line 11 of Table 18.8.1, now shown with explicit normalization for the measure

\,\mathrm{d}r

. … ►and thus replacing

p

n-l-1

as in Table 18.8.1, line 11, or as in (18.39.33), … ►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry. …

28: Errata

… ►

Equation (34.7.4)

34.7.4

\begin{pmatrix}j_{13}&j_{23}&j_{33}\\ m_{13}&m_{23}&m_{33}\end{pmatrix}\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{m_{r1},m_{r2},r=1,2,3}\begin{pmatrix}j% _{11}&j_{12}&j_{13}\\ m_{11}&m_{12}&m_{13}\end{pmatrix}\*\begin{pmatrix}j_{21}&j_{22}&j_{23}\\ m_{21}&m_{22}&m_{23}\end{pmatrix}\begin{pmatrix}j_{31}&j_{32}&j_{33}\\ m_{31}&m_{32}&m_{33}\end{pmatrix}\*\begin{pmatrix}j_{11}&j_{21}&j_{31}\\ m_{11}&m_{21}&m_{31}\end{pmatrix}\begin{pmatrix}j_{12}&j_{22}&j_{32}\\ m_{12}&m_{22}&m_{32}\end{pmatrix}

Originally the third $\mathit{3j}$ symbol in the summation was written incorrectly as $\begin{pmatrix}j_{31}&j_{32}&j_{33}\\ m_{13}&m_{23}&m_{33}\end{pmatrix}.$

Reported 2015-01-19 by Yan-Rui Liu.

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Version 1.0.9 (August 29, 2014)

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Version 1.0.8 (April 25, 2014)

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Version 1.0.7 (March 21, 2014)

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Version 1.0.3 (Aug 29, 2011)

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29: 18.15 Asymptotic Approximations

… ►See also Dunster (1999), Atia et al. (2014) and Temme (2015, Chapter 32).

30: 10.22 Integrals

… ►For asymptotic expansions of Hankel transforms see Wong (1976, 1977), Frenzen and Wong (1985a) and Galapon and Martinez (2014). …