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21: Bibliography F

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Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water. J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.

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Document

Referenced by:

§36.14(iv).

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Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface. J. Acoust. Soc. Amer. 95 (2), pp. 650–660.

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Document

Referenced by:

§36.14(iv).

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22: Bibliography J

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Tables of Functions with Formulae and Curves. 4th edition, Dover Publications, New York.

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Notes:

Contains corrections and enlargements of earlier editions. Originally published by B. G. Teubner, Leipzig, in 1933. In German and English.

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MathReview, ZentralBlatt

Referenced by:

2nd item, §20.15, §5.1, Notations P, E. Jahnke, F. Emde, and F. Lösch (1966).

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23: 10.20 Uniform Asymptotic Expansions for Large Order

… ►The equations of the curved boundaries $D_1{E}_1$ and $D_2{E}_2$ in the $\zeta$-plane are given parametrically by … ►The curves $B{P}_1{E}_1$ and $B{P}_2{E}_2$ in the $z$-plane are the inverse maps of the line segments …The points $P_1,P_2$ where these curves intersect the imaginary axis are $\pm \mathrm{i}c$, where …

24: 28.33 Physical Applications

… ►For points $(q,a)$ that are at intersections of $ℒ$ with the characteristic curves $a=a_n\left(q\right)$ or $a=b_n\left(q\right)$, a periodic solution is possible. …

25: Bibliography T

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Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves. Trans. Amer. Math. Soc. 365 (12), pp. 6697–6729.

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ISSN 0002-9947, Document, FullText, MathReview (John M. Voight), ZentralBlatt

Referenced by:

§15.8(v), §15.8(v).

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26: 18.39 Applications in the Physical Sciences

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Figure 18.39.2: Coulomb–Pollaczek weight functions, $x\in [-1,1]$, (18.39.50) for $s=10$, $l=0$, and $Z=\pm 1$. For $Z=+1$ the weight function, red curve, has an essential singularity at $x=-1$, as all derivatives vanish as $x\to -1+$; the green curve is ${\int }_{-1}^x{w}^{\mathrm{CP}}(y)dy$, to be compared with its histogram approximation in §18.40(ii). For $Z=-1$ the weight function, blue curve, is non-zero at $x=-1$, but this point is also an essential singularity as the discrete parts of the weight function of (18.39.51) accumulate as $k\to \mathrm{\infty }$, $x_k\to -1-$. Magnify

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27: Bibliography M

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Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of ${𝐏}^2$ . In Geometry of Differential Equations, A. Khovanskii, A. Varchenko, and V. Vassiliev (Eds.), Amer. Math. Soc. Transl. Ser. 2, Vol. 186, pp. 131–151.

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External Links:

MathReview (Bruce Hunt), ZentralBlatt

Referenced by:

§32.2(iv).

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Elliptic Curves. Cambridge University Press, Cambridge.

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Notes:

Reprint with corrections of original edition, published in 1997 by Cambridge University Press

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ISBN 0-521-58228-8; 0-521-65817-9, MathReview (Amílcar Pacheco), ZentralBlatt

Referenced by:

§20.1, §20.11(i), §20.11(ii), §20.12(i), §20.12(i), §20.12(ii), §20.7(iii), §20.7(v), §20.9(i), §20.9(ii), Ch.20, §22.18(ii), §22.18(iv), Ch.22, §23.1, §23.15(i), §23.20(i), §23.20(ii), §23.20(ii), §23.21(ii), §23.22(ii), §23.6(iv), Ch.23, Notations T.

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Table of the ratio: Area to bounding ordinate, for any portion of normal curve. Biometrika 18, pp. 395–400.

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FullText, ZentralBlatt

Referenced by:

§7.8.

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28: 4.13 Lambert $W$-Function

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Figure 4.13.2: The $W\left(z\right)$ function on the first 5 Riemann sheets. $W\left(z\right)$ maps the first Riemann sheet in the middle of the left-hand side to the region enclosed by the green curve on the right-hand side; it maps the Riemann sheet on the left-hand side to the region enclosed by the pink, green and orange curves on the right-hand side, etc. Magnify

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29: Bibliography H

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Inverse virial symmetry of diatomic potential curves. J. Chem. Phys. 109 (1), pp. 11–19.

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Document

Referenced by:

§15.18.

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30: Bibliography W

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Caustics: Mathematical curves generated by light shined through rippled plastic. Scientific American 249, pp. 146–153.

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Referenced by:

§36.14(ii).

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