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21—30 of 168 matching pages

21: 24.2 Definitions and Generating Functions

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Table 24.2.5: Coefficients

b_{n,k}

of the Bernoulli polynomials

B_{n}\left(x\right)=\sum_{k=0}^{n}b_{n,k}x^{k}

► ►►►►►

	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…
$11$	$0$	$\tfrac{5}{6}$	$0$	$-\tfrac{11}{2}$	$0$	$11$	$0$	$-11$	$0$	$\tfrac{55}{6}$	$-\tfrac{11}{2}$	$1$
$12$	$-\tfrac{691}{2730}$	$0$	$5$	$0$	$-\tfrac{33}{2}$	$0$	$22$	$0$	$-\tfrac{33}{2}$	$0$	$11$	$-6$	$1$
…

► ►

Table 24.2.6: Coefficients

e_{n,k}

of the Euler polynomials

E_{n}\left(x\right)=\sum_{k=0}^{n}e_{n,k}x^{k}

► ►►►►

	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…
$11$	$\tfrac{691}{4}$	$0$	$-\tfrac{1705}{2}$	$0$	$\tfrac{2805}{4}$	$0$	$-231$	$0$	$\tfrac{165}{4}$	$0$	$-\tfrac{11}{2}$	$1$
…

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22: 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.

ⓘ

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

…

23: 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.

ⓘ

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.

ⓘ

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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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,

ⓘ

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

►

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,

ⓘ

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

… ►

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,

ⓘ

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

►

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,

ⓘ

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,

ⓘ

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

…

25: 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.

ⓘ

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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R. Wong and Y. Zhao (2002a) Exponential asymptotics of the Mittag-Leffler function. Constr. Approx. 18 (3), pp. 355–385.

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External Links:: ISSN 0176-4276, Document, MathReview, ZentralBlatt
Referenced by:: §10.46.
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

…

26: 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.

ⓘ

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

… ►

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

…

27: 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}.

ⓘ

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

… ►

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}}.

ⓘ

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

… ►

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}.

ⓘ

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

… ►

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}.

ⓘ

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

►

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

28: Bibliography E

… ►

C. Eckart (1930) The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.

ⓘ

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

… ►

A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1953b) Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:: Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.
External Links:: MathReview (E. T. Copson), ZentralBlatt
Referenced by:: §10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), (18.17.21_1), §18.17(iv), §18.17(i), §18.17(viii), (18.35.1), (18.35.2), (18.35.4_5), §18.35(i), (18.5.11_1), (18.5.11_3), §18.5(ii), §18.9(iii), §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.
Encodings:: BibTeX

… ►

F. H. L. Essler, H. Frahm, A. R. Its, and V. E. Korepin (1996) Painlevé transcendent describes quantum correlation function of the

X X Z

antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.

ⓘ

External Links:: ISSN 0305-4470, Document, MathReview (Estelle L. Basor), ZentralBlatt
Referenced by:: §32.16.
Encodings:: BibTeX

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L. Euler (1768) Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.

ⓘ

Referenced by:: §25.12(i).
Encodings:: BibTeX

…

29: Bibliography M

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M. Mazzocco (2001a) Rational solutions of the Painlevé VI equation. J. Phys. A 34 (11), pp. 2281–2294.

ⓘ

External Links:: ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt
Referenced by:: §32.8(vi).
Encodings:: BibTeX

… ►

T. Morita (1978) Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

ⓘ

Notes:: An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.
External Links:: ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt
Referenced by:: §19.36(ii), §19.39(ii).
Encodings:: BibTeX

… ►

L. Moser and M. Wyman (1958b) Stirling numbers of the second kind. Duke Math. J. 25 (1), pp. 29–43.

ⓘ

External Links:: Document, MathReview (A. Sade), ZentralBlatt
Referenced by:: §26.1, §26.8(vii), Notations S.
Encodings:: BibTeX

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D. Müller, B. G. Kelly, and J. J. O’Brien (1994) Spheroidal eigenfunctions of the tidal equation. Phys. Rev. Lett. 73 (11), pp. 1557–1560.

ⓘ

External Links:: ISSN 0031-9007, Document, MathReview, ZentralBlatt
Referenced by:: §30.13(v).
Encodings:: BibTeX

… ►

L. A. Muraveĭ (1976) Zeros of the function

Ai^{\prime}(z)-\sigma Ai(z)

. Differential Equations 11, pp. 797–811.

ⓘ

External Links:: ZentralBlatt
Referenced by:: §9.9(i).
Encodings:: BibTeX

…

30: Bibliography C

… ►

L. Carlitz (1960) Note on Nörlund’s polynomial

B_{n}^{(z)}

. Proc. Amer. Math. Soc. 11 (3), pp. 452–455.

ⓘ

External Links:: FullText, MathReview (M. P. Drazin), ZentralBlatt
Referenced by:: §26.1, §26.1, Notations S, Notations S.
Encodings:: BibTeX

… ►

P. A. Clarkson (2003b) The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

ⓘ

External Links:: ISSN 0022-2488, Document, MathReview, ZentralBlatt
Referenced by:: §32.8(iv).
Encodings:: BibTeX

… ►

J. A. Cochran (1963) Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

ⓘ

External Links:: ISSN 0018-9480, FullText
Referenced by:: §10.21(x).
Encodings:: BibTeX

… ►

M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

ⓘ

External Links:: ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §13.29(v), §15.19(v).
Encodings:: BibTeX

… ►

F. Cooper, A. Khare, and A. Saxena (2006) Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

ⓘ

External Links:: ISSN 1076-2787, Document, MathReview
Referenced by:: §19.6(i).
Encodings:: BibTeX

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