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21: Bibliography T

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On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes. Phys. A 244 (1-4), pp. 402–413.

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ISSN 0378-4371, Document, MathReview (Vitor R. Vieira)

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§32.11(iv).

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Iterative Methods for the Solution of Equations. Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..

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MathReview (W. C. Rheinboldt), ZentralBlatt

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§3.8(iii).

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Rational Chebyshev approximation for the Fermi-Dirac integral $F_{-3/2}(x)$ . Solid–State Electronics 41 (5), pp. 771–773.

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Document

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§25.21(vii).

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Asymptotic solution of a linear nonhomogeneous second order differential equation with a transition point and its application to the computations of toroidal shells and propeller blades. J. Appl. Math. Mech. 23, pp. 1549–1565.

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Document, MathReview (F. W. J. Olver), ZentralBlatt

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§9.1, Notations E, Notations E.

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22: 23.20 Mathematical Applications

… ►If $a,b\in \mathbb{Q}$, then by rescaling we may assume $a,b\in \mathbb{Z}$. Let $T$ denote the set of points on $C$ that are of finite order (that is, those points $P$ for which there exists a positive integer $n$ with $nP=o$), and let $I,K$ be the sets of points with integer and rational coordinates, respectively. …Values of $x$ are then found as integer solutions of $x^3+ax+b-y^2=0$ (in particular $x$ must be a divisor of $b-y^2$). … ►For further information, including the application of (23.20.7) to the solution of the general quintic equation, see Borwein and Borwein (1987, Chapter 4). …

23: Bibliography H

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High frequency solutions of the delta wing equations. Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.

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ISSN 0308-2105, MathReview (V. M. Babich), ZentralBlatt

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§29.19(ii).

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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

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ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

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§32.11(ii).

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Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems. Ph.D. Thesis, Technischen Universität Berlin.

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Notes:

(All relevant material, plus corrections, are included in Deconinck et al. (2004).)

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ZentralBlatt

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§21.5(i).

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Über die Integration logarithmisch-rationaler Differentiale. J. Reine Angew. Math. 3, pp. 101–159.

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ZentralBlatt

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§25.12(i).

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Solutions of Poisson’s equation in channel-like geometries. Comput. Phys. Comm. 115 (1), pp. 45–68.

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ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt

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§14.31(i).

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24: Mathematical Introduction

… ►These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3). … ► ►►►

$(a,b]$ or $[a,b)$	half-closed intervals.
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$\mathbb{Q}$	set of all rational numbers.
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25: Bibliography L

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The solutions of the Mathieu equation with a complex variable and at least one parameter large. Trans. Amer. Math. Soc. 36 (3), pp. 637–695.

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ISSN 0002-9947, FullText, MathReview Entry, ZentralBlatt

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§28.8(iv).

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Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178 (2), pp. 425–452.

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For a Maple implementation of the algorithm given in this paper for Jack and zonal polynomials see Zeilberger (website).

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ISSN 0010-3616, Link, MathReview (Kazuhiro Hikami), ZentralBlatt

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§35.12.

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Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equations 162 (1), pp. 27–63.

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ISSN 0022-0396, Document, MathReview (John Albert), ZentralBlatt

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§22.19(iii).

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Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.

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MathReview (F. Gotze), ZentralBlatt

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§13.31(iii).

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Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.

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ISSN 0029-599X, Document, MathReview (Vítĕzslav Veselý), ZentralBlatt

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§10.74(vii).

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26: Bibliography R

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Rational Chebyshev approximation by Remes’ algorithms. Numer. Math. 7 (4), pp. 322–330.

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ISSN 0029-599X, Document, MathReview (C. W. Clenshaw), ZentralBlatt

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§3.11(i).

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Composite approximations to the solutions of the Orr-Sommerfeld equation. Studies in Appl. Math. 51, pp. 341–368.

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MathReview (E. A. Boyd), ZentralBlatt

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(9.13.25), (9.13.26), (9.13.28), (9.13.29), (9.13.32), (9.13.33), (9.13.34), §9.13(ii), §9.13(ii).

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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow. Studies in Appl. Math. 53, pp. 91–110.

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MathReview (T. W. Kao), ZentralBlatt

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§2.8(iii).

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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory. Studies in Appl. Math. 53, pp. 217–224.

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MathReview (T. W. Kao), ZentralBlatt

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§2.8(iii).

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Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations. Technical Reports and Memoranda Technical Report 2865, Aeronautical Research Council (Great Britain).

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Notes:

Reprinted by Her Majesty’s Stationery Office, London, 1962.

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MathReview (P. Germain)

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§29.19(ii).

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27: Bibliography J

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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II. Phys. D 2 (3), pp. 407–448.

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ISSN 0167-2789, Document, MathReview (V. A. Golubeva), ZentralBlatt

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§32.4(i), §32.4(ii), §32.4(iv), §32.4(v), §32.6(ii), §32.6(iii), §32.6(iv), §32.6(v), §32.6(v), §32.6(v).

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REMES2 — a Fortran program to calculate rational minimax approximations to a given function. Technical Report Technical Report AECL-4210, Atomic Energy of Canada Limited. Chalk River Nuclear Laboratories, Chalk River, Ontario.

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§3.11(iii).

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On Boutroux’s tritronquée solutions of the first Painlevé equation. Stud. Appl. Math. 107 (3), pp. 253–291.

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ISSN 0022-2526, Document, MathReview, ZentralBlatt

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§32.12(i).

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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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ISSN 0075-4102, Document, MathReview (Mehmet Can), ZentralBlatt

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§32.11(i).

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28: Bibliography W

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Rational approximations for the modified Bessel function of the second kind. Comput. Phys. Comm. 59 (3), pp. 471–493.

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ISSN 0010-4655, Document, MathReview, ZentralBlatt

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§10.76(ii).

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A rational approximant for the digamma function. Numer. Algorithms 33 (1-4), pp. 499–507.

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International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

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§3.9(vi), §5.23(i).

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Rational Chebyshev approximation. Numer. Math. 10 (4), pp. 289–306.

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ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.11(iii).

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Rational function certification of multisum/integral/“$q$” identities. Bull. Amer. Math. Soc. (N.S.) 27 (1), pp. 148–153.

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ISSN 0273-0979, Pdf, Document, MathReview (Robert A. Gustafson), ZentralBlatt

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§16.4(iii).

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Rational Chebyshev approximations for the Bessel functions $J_0(x)$, $J_1(x)$, $Y_0(x)$, $Y_1(x)$ . Math. Comp. 39 (160), pp. 617–623.

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Tables on microfiche

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ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt

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9th item.

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