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21—30 of 187 matching pages

21: Bibliography H

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V. B. Headley and V. K. Barwell (1975) On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.

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External Links:: FullText, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §9.13(i).
Encodings:: BibTeX

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D. R. Herrick and S. O’Connor (1998) Inverse virial symmetry of diatomic potential curves. J. Chem. Phys. 109 (1), pp. 11–19.

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External Links:: Document
Referenced by:: §15.18.
Encodings:: BibTeX

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H. W. Hethcote (1970) Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.

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External Links:: Document, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §10.21(xiv).
Encodings:: BibTeX

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G. W. Hill (1970) Algorithm 395: Student’s t-distribution. Comm. ACM 13 (10), pp. 617–619.

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Notes:: Includes Algol program, maximum accuracy 11S. For Remarks see ACM Trans. Math. Software 5(1979) and 7(1981)
External Links:: ISSN 0001-0782, Document, Remark 1, Remark 2
Referenced by:: §8.28(iv).
Encodings:: BibTeX

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K. Horata (1989) An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.

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External Links:: ZentralBlatt
Referenced by:: §24.6.
Encodings:: BibTeX

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22: Bibliography F

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V. N. Faddeyeva and N. M. Terent’ev (1961) Tables of Values of the Function

w(z)=e^{-z^{2}}(1+2i\pi^{-1/2}\int_{0}^{z}e^{t^{2}}dt)

for Complex Argument. Edited by V. A. Fok; translated from the Russian by D. G. Fry. Mathematical Tables Series, Vol. 11, Pergamon Press, Oxford.

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External Links:: MathReview, ZentralBlatt
Referenced by:: V. N. Faddeeva and N. M. Terent’ev (1954).
Encodings:: BibTeX

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N. Fleury and A. Turbiner (1994) Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.

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External Links:: ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt
Referenced by:: §13.3(ii), §15.5(i), §16.3(i).
Encodings:: BibTeX

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A. S. Fokas and M. J. Ablowitz (1982) On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.

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External Links:: ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt
Referenced by:: §32.13(i), §32.7(i), §32.7(iii).
Encodings:: BibTeX

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P. J. Forrester and N. S. Witte (2004) Application of the

\tau

-function theory of Painlevé equations to random matrices:

\rm P_{\rm VI}

, the JUE, CyUE, cJUE and scaled limits. Nagoya Math. J. 174, pp. 29–114.

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External Links:: ISSN 0027-7630, MathReview, ZentralBlatt
Referenced by:: §32.10(vi), §32.6(v).
Encodings:: BibTeX

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L. W. Fullerton (1972) Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

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Notes:: Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.
External Links:: ISSN 0001-0782, Document, Remark
Referenced by:: §8.28(ii).
Encodings:: BibTeX

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23: Bibliography B

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R. Barakat (1961) Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

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External Links:: FullText, MathReview (J. C. P. Miller), ZentralBlatt
Referenced by:: §8.7.
Encodings:: BibTeX

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B. C. Berndt, S. Bhargava, and F. G. Garvan (1995) Ramanujan’s theories of elliptic functions to alternative bases. Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.

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External Links:: ISSN 0002-9947, FullText, MathReview (J. Borwein), ZentralBlatt
Referenced by:: §15.8(v), §20.11(iii).
Encodings:: BibTeX

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F. Bethuel (1998) Vortices in Ginzburg-Landau Equations. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), pp. 11–19.

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External Links:: ISSN 1431-0643, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §17.17.
Encodings:: BibTeX

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A. Bhattacharyya and L. Shafai (1988) Theoretical and experimental investigation of the elliptical annual ring antenna. IEEE Trans. Antennas and Propagation 36 (11), pp. 1526–1530.

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External Links:: Document
Referenced by:: 5th item.
Encodings:: BibTeX

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R. L. Bishop (1981) Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).

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External Links:: ISSN 0035-9149, Document, MathReview
Referenced by:: Sidebar 9.SB1.
Encodings:: BibTeX

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24: 28.6 Expansions for Small $q$

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28.6.2

a_{1}\left(q\right)=1+q-\tfrac{1}{8}q^{2}-\tfrac{1}{64}q^{3}-\tfrac{1}{1536}q^% {4}+\tfrac{11}{36864}q^{5}+\tfrac{49}{5\;89824}q^{6}+\tfrac{55}{94\;37184}q^{7% }-\tfrac{83}{353\;89440}q^{8}+\cdots,

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Symbols:: $a_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation and $q=h^{2}$ : parameter
Permalink:: http://dlmf.nist.gov/28.6.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §28.6(i), §28.6 and Ch.28

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28.6.3

b_{1}\left(q\right)=1-q-\tfrac{1}{8}q^{2}+\tfrac{1}{64}q^{3}-\tfrac{1}{1536}q^% {4}-\tfrac{11}{36864}q^{5}+\tfrac{49}{5\;89824}q^{6}-\tfrac{55}{94\;37184}q^{7% }-\tfrac{83}{353\;89440}q^{8}+\cdots,

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Symbols:: $b_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation and $q=h^{2}$ : parameter
Permalink:: http://dlmf.nist.gov/28.6.E3
Encodings:: pMML, png, TeX
See also:: Annotations for §28.6(i), §28.6 and Ch.28

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28.6.10

a_{5}\left(q\right)=25+\tfrac{1}{48}q^{2}+\tfrac{11}{7\;74144}q^{4}+\tfrac{1}{% 1\;47456}q^{5}+\tfrac{37}{8918\;13888}q^{6}+\cdots,

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Symbols:: $a_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation and $q=h^{2}$ : parameter
Permalink:: http://dlmf.nist.gov/28.6.E10
Encodings:: pMML, png, TeX
See also:: Annotations for §28.6(i), §28.6 and Ch.28

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28.6.11

b_{5}\left(q\right)=25+\tfrac{1}{48}q^{2}+\tfrac{11}{7\;74144}q^{4}-\tfrac{1}{% 1\;47456}q^{5}+\tfrac{37}{8918\;13888}q^{6}+\cdots,

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Symbols:: $b_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation and $q=h^{2}$ : parameter
Permalink:: http://dlmf.nist.gov/28.6.E11
Encodings:: pMML, png, TeX
See also:: Annotations for §28.6(i), §28.6 and Ch.28

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28.6.21

2^{\ifrac{1}{2}}\operatorname{ce}_{0}\left(z,q\right)=1-\tfrac{1}{2}q\cos 2z+% \tfrac{1}{32}q^{2}\left(\cos 4z-2\right)-\tfrac{1}{128}q^{3}\left(\tfrac{1}{9}% \cos 6z-11\cos 2z\right)+\cdots,

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Symbols:: $\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : Mathieu function, $\cos\NVar{z}$ : cosine function, $q=h^{2}$ : parameter and $z$ : complex variable
A&S Ref:: 20.2.27
Referenced by:: §28.6(ii)
Permalink:: http://dlmf.nist.gov/28.6.E21
Encodings:: pMML, png, TeX
See also:: Annotations for §28.6(ii), §28.6 and Ch.28

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25: Bibliography J

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F. Johansson (2012) Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS J. Comput. Math. 15, pp. 341–359.

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External Links:: ISSN 1461-1570, Document, Link, MathReview (Tim Huber), ZentralBlatt
Referenced by:: §27.20.
Encodings:: BibTeX

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W. B. Jones and W. J. Thron (1980) Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications, Vol. 11, Addison-Wesley Publishing Co., Reading, MA.

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External Links:: ISBN 0-201-13510-8, MathReview (E. Frank), ZentralBlatt
Referenced by:: §1.12(ii), §1.12(iii), §1.12(iv), §1.12(v), §13.17, §13.17, §13.5, §13.5, §4.25, §5.10.
Encodings:: BibTeX

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N. Joshi and A. V. Kitaev (2005) The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis. J. Reine Angew. Math. 583, pp. 29–86.

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External Links:: ISSN 0075-4102, Document, MathReview (Mehmet Can), ZentralBlatt
Referenced by:: §32.11(i).
Encodings:: BibTeX

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26: 1.3 Determinants, Linear Operators, and Spectral Expansions

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1.3.1

\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}.

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Symbols:: $\det$ : determinant, $j$ : integer and $k$ : integer
Permalink:: http://dlmf.nist.gov/1.3.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

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1.3.2

\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{vmatrix}=a_{11}\begin{vmatrix}a_{22}&a_{23}\\ a_{32}&a_{33}\end{vmatrix}-a_{12}\begin{vmatrix}a_{21}&a_{23}\\ a_{31}&a_{33}\end{vmatrix}+a_{13}\begin{vmatrix}a_{21}&a_{22}\\ a_{31}&a_{32}\end{vmatrix}=a_{11}a_{22}a_{33}-a_{11}a_{23}a_{32}-a_{12}a_{21}a% _{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{13}a_{22}a_{31}.

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Symbols:: $\det$ : determinant, $j$ : integer and $k$ : integer
Permalink:: http://dlmf.nist.gov/1.3.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

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1.3.8

{\begin{vmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{vmatrix}}^{2}\leq(a^{2}_{11}+a^{2}_{12})(a^{2}_{21}+a^{2}_{2% 2}),

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Symbols:: $\det$ : determinant
Permalink:: http://dlmf.nist.gov/1.3.E8
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

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27: Bibliography W

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R. J. Wells (1999) Rapid approximation to the Voigt/Faddeeva function and its derivatives. J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.

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Notes:: Includes Fortran code in the appendices to compute the functions to an accuracy between $10^{-2}$ and $10^{-5}$ .
External Links:: ISSN 0022-4073, Document
Referenced by:: §7.21, §7.21.
Encodings:: BibTeX

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J. A. Wilson (1980) Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.

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External Links:: ISSN 0036-1410, Document, MathReview (R. G. Buschman), ZentralBlatt
Referenced by:: §18.25(i), §18.25(i), §18.25(ii), §18.25(iii), §18.26(i), §18.26(ii), §18.38(iii).
Encodings:: BibTeX

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G. Wolf (2008) On the asymptotic behavior of the Fourier coefficients of Mathieu functions. J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.

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External Links:: ISSN 1044-677X, FullText
Referenced by:: §28.4(vii).
Encodings:: BibTeX

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E. M. Wright (1940b) The generalized Bessel function of order greater than one. Quart. J. Math., Oxford Ser. 11, pp. 36–48.

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External Links:: Document, MathReview (M. C. Gray), ZentralBlatt
Referenced by:: §10.46.
Encodings:: BibTeX

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Makinouchi (1966) tabulates all values of $j_{\nu,m}$ and $y_{\nu,m}$ in the interval $(0,100)$ , with at least 29S. These are for $\nu=0(1)5$ , 10, 20; $\nu=\tfrac{3}{2}$ , $\tfrac{5}{2}$ ; $\nu=m/n$ with $m=1(1)n-1$ and $n=3(1)8$ , except for $\nu=\tfrac{1}{2}$ .

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•

Zhang and Jin (1996, p. 199) tabulates the real and imaginary parts of the first 15 conjugate pairs of complex zeros of $Y_{0}\left(z\right)$ , $Y_{1}\left(z\right)$ , $Y_{1}'\left(z\right)$ and the corresponding values of $Y_{1}\left(z\right)$ , $Y_{0}\left(z\right)$ , $Y_{1}\left(z\right)$ , respectively, 10D.

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•

Abramowitz and Stegun (1964, Chapter 11) tabulates $\int_{0}^{x}J_{0}\left(t\right)\,\mathrm{d}t$ , $\int_{0}^{x}Y_{0}\left(t\right)\,\mathrm{d}t$ , $x=0(.1)10$ , 10D; $\int_{0}^{x}t^{-1}(1-J_{0}\left(t\right))\,\mathrm{d}t$ , $\int_{x}^{\infty}t^{-1}Y_{0}\left(t\right)\,\mathrm{d}t$ , $x=0(.1)5$ , 8D.

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•

Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of $K_{n}\left(z\right)$ , for $n=2(1)10$ , 29S.

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•

Abramowitz and Stegun (1964, Chapter 11) tabulates $e^{-x}\int_{0}^{x}I_{0}\left(t\right)\,\mathrm{d}t$ , $e^{x}\int_{x}^{\infty}K_{0}\left(t\right)\,\mathrm{d}t$ , $x=0(.1)10$ , 7D; $e^{-x}\int_{0}^{x}t^{-1}(I_{0}\left(t\right)-1)\,\mathrm{d}t$ , $xe^{x}\int_{x}^{\infty}t^{-1}K_{0}\left(t\right)\,\mathrm{d}t$ , $x=0(.1)5$ , 6D.

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29: Bibliography S

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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

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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

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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.

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

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K. Soni (1980) Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels. SIAM J. Math. Anal. 11 (5), pp. 828–841.

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External Links:: ISSN 0036-1410, Document, MathReview (John S. Lew), ZentralBlatt
Referenced by:: §2.5(ii).
Encodings:: BibTeX

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30: 34.7 Basic Properties: $\mathit{9j}$ Symbol

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34.7.1

\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{13}\\ j_{31}&j_{31}&0\end{Bmatrix}=\frac{(-1)^{j_{12}+j_{21}+j_{13}+j_{31}}}{((2j_{1% 3}+1)(2j_{31}+1))^{\frac{1}{2}}}\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{22}&j_{21}&j_{31}\end{Bmatrix}.

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Symbols:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol, $\begin{Bmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{l_{1}}&\NVar{l_{2}}&\NVar{l_{3}}\end{Bmatrix}$ : $\mathit{6j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Permalink:: http://dlmf.nist.gov/34.7.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §34.7(i), §34.7 and Ch.34

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34.7.2

\sum_{j_{12}\,j_{34}}(2j_{12}+1)(2j_{34}+1)(2j_{13}+1)(2j_{24}+1)\begin{% Bmatrix}j_{1}&j_{2}&j_{12}\\ j_{3}&j_{4}&j_{34}\\ j_{13}&j_{24}&j\end{Bmatrix}\begin{Bmatrix}j_{1}&j_{2}&j_{12}\\ j_{3}&j_{4}&j_{34}\\ j^{\prime}_{13}&j^{\prime}_{24}&j\end{Bmatrix}=\delta_{j_{13},j^{\prime}_{13}}% \delta_{j_{24},j^{\prime}_{24}}.

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Symbols:: $\delta_{\NVar{j},\NVar{k}}$ : Kronecker delta, $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Permalink:: http://dlmf.nist.gov/34.7.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §34.7(iv), §34.7 and Ch.34

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34.7.3

\sum_{j_{13}\,j_{24}}(-1)^{2j_{2}+j_{24}+j_{23}-j_{34}}(2j_{13}+1)(2j_{24}+1)% \begin{Bmatrix}j_{1}&j_{2}&j_{12}\\ j_{3}&j_{4}&j_{34}\\ j_{13}&j_{24}&j\end{Bmatrix}\begin{Bmatrix}j_{1}&j_{3}&j_{13}\\ j_{4}&j_{2}&j_{24}\\ j_{14}&j_{23}&j\end{Bmatrix}=\begin{Bmatrix}j_{1}&j_{2}&j_{12}\\ j_{4}&j_{3}&j_{34}\\ j_{14}&j_{23}&j\end{Bmatrix}.

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Symbols:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Referenced by:: §34.9
Permalink:: http://dlmf.nist.gov/34.7.E3
Encodings:: pMML, png, TeX
See also:: Annotations for §34.7(vi), §34.7 and Ch.34

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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}.

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Symbols:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol, $\begin{pmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{m_{1}}&\NVar{m_{2}}&\NVar{m_{3}}\end{pmatrix}$ : $\mathit{3j}$ symbol, $j,j_{r}$ : non-negative integers or non-negative integers plus one half. and $r$ : nonnegative integer
Referenced by:: Erratum (V1.0.10) for Equation (34.7.4)
Permalink:: http://dlmf.nist.gov/34.7.E4
Encodings:: pMML, png, TeX
Errata (effective with 1.0.10):: 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
See also:: Annotations for §34.7(vi), §34.7 and Ch.34

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34.7.5

\sum_{j^{\prime}}(2j^{\prime}+1)\begin{Bmatrix}j_{11}&j_{12}&j^{\prime}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}\begin{Bmatrix}j_{11}&j_{12}&j^{\prime}\\ j_{23}&j_{33}&j\end{Bmatrix}={(-1)^{2j}}\begin{Bmatrix}j_{21}&j_{22}&j_{23}\\ j_{12}&j&j_{32}\end{Bmatrix}\begin{Bmatrix}j_{31}&j_{32}&j_{33}\\ j&j_{11}&j_{21}\end{Bmatrix}.

ⓘ

Symbols:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol, $\begin{Bmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{l_{1}}&\NVar{l_{2}}&\NVar{l_{3}}\end{Bmatrix}$ : $\mathit{6j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Permalink:: http://dlmf.nist.gov/34.7.E5
Encodings:: pMML, png, TeX
See also:: Annotations for §34.7(vi), §34.7 and Ch.34