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41—48 of 48 matching pages

	Open Source	With Book	Commercial
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33 Coulomb Functions
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42: Bibliography L

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A. Laforgia and S. Sismondi (1988) Monotonicity results and inequalities for the gamma and error functions. J. Comput. Appl. Math. 23 (1), pp. 25–33.

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External Links:: ISSN 0377-0427, Document, MathReview (M. E. Cohen), ZentralBlatt
Referenced by:: §7.8.
Encodings:: BibTeX

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K. V. Leung and S. S. Ghaderpanah (1979) An application of the finite element approximation method to find the complex zeros of the modified Bessel function

K_{n}(z)

. Math. Comp. 33 (148), pp. 1299–1306.

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External Links:: ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt
Referenced by:: §10.74(vi), 2nd item.
Encodings:: BibTeX

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$n$	$\operatorname{pp}\left(n\right)$	$n$	$\operatorname{pp}\left(n\right)$	$n$	$\operatorname{pp}\left(n\right)$
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16	11297	33	189 74973	50	1 04996 40707

44: 28.8 Asymptotic Expansions for Large $q$

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28.8.1

\rselection{a_{m}\left(h^{2}\right)\\ b_{m+1}\left(h^{2}\right)}\sim-2h^{2}+2sh-\frac{1}{8}(s^{2}+1)-\frac{1}{2^{7}h% }(s^{3}+3s)-\frac{1}{2^{12}h^{2}}(5s^{4}+34s^{2}+9)-\frac{1}{2^{17}h^{3}}(33s^% {5}+410s^{3}+405s)-\frac{1}{2^{20}h^{4}}(63s^{6}+1260s^{4}+2943s^{2}+486)-% \frac{1}{2^{25}h^{5}}(527s^{7}+15617s^{5}+69001s^{3}+41607s)+\cdots.

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Symbols:: $a_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation, $b_{\NVar{n}}\left(\NVar{q}\right)$ : eigenvalues of Mathieu equation, $\sim$ : Poincaré asymptotic expansion, $m$ : integer and $h$ : parameter
A&S Ref:: 20.2.30 (in different form)
Referenced by:: §28.8(i), Erratum (V1.1.10) for Sections 28.6(i), 28.6(ii), 28.8(i), 28.8(ii)
Permalink:: http://dlmf.nist.gov/28.8.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §28.8(i), §28.8 and Ch.28

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A. S. Fokas, A. R. Its, and X. Zhou (1992) Continuous and Discrete Painlevé Equations. In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 33–47.

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Notes:: Proc. NATO Adv. Res. Workshop, Sainte-Adèle, Canada, 1990
External Links:: MathReview (F. Pempinelli), ZentralBlatt
Referenced by:: §32.15.
Encodings:: BibTeX

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46: Errata

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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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47: 4.23 Inverse Trigonometric Functions

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48: Bibliography S

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G. Szegő (1933) Asymptotische Entwicklungen der Jacobischen Polynome. Schr. der König. Gelehr. Gesell. Naturwiss. Kl. 10, pp. 33–112.

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External Links:: ZentralBlatt
Referenced by:: §18.15(ii).
Encodings:: BibTeX

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梅州麻将游戏大厅,网上梅州麻将游戏规则,【复制打开网址：33kk55.com】正规博彩平台,在线赌博平台,梅州麻将游戏玩法介绍,真人梅州麻将游戏规则,网上真人棋牌游戏平台,真人博彩游戏平台网址YBMNMhMhMMyNXMsX

41—48 of 48 matching pages

41: Software Index

42: Bibliography L

43: 26.12 Plane Partitions

44: 28.8 Asymptotic Expansions for Large $q$

45: Bibliography F

46: Errata

47: 4.23 Inverse Trigonometric Functions

48: Bibliography S

梅州麻将游戏大厅,网上梅州麻将游戏规则,【复制打开网址：33kk55.com】正规博彩平台,在线赌博平台,梅州麻将游戏玩法介绍,真人梅州麻将游戏规则,网上真人棋牌游戏平台,真人博彩游戏平台网址YBMNMhMhMMyNXMsX

41—48 of 48 matching pages

41: Software Index

42: Bibliography L

43: 26.12 Plane Partitions

44: 28.8 Asymptotic Expansions for Large q

45: Bibliography F

46: Errata

47: 4.23 Inverse Trigonometric Functions

48: Bibliography S

44: 28.8 Asymptotic Expansions for Large $q$