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11: Bibliography E

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Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.

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ISBN 3-540-60230-5, MathReview (Alfred Actor), ZentralBlatt

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§25.17.

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Waring’s problem. Amer. Math. Monthly 78 (1), pp. 10–36.

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Document, FullText, MathReview (J. W. S. Cassels), ZentralBlatt

Referenced by:

§27.13(iii), §27.13(iii).

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The Sobolev orthogonality and spectral analysis of the Laguerre polynomials $\{L_n^{-k}\}$ for positive integers $k$ . J. Comput. Appl. Math. 171 (1-2), pp. 199–234.

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ISSN 0377-0427, Document, Link, MathReview (Khélifa Trimèche)

Referenced by:

§18.36(v).

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12: Bibliography R

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

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English translation, AEC-TR-4491, United States Atomic Energy Commission

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MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

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The problem of an infinite plate under an inclined loading, with tables of the integrals of $\mathrm{Ai}(\pm \mathrm{x})$ and $\mathrm{Bi}(\pm \mathrm{x})$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.

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Document, MathReview (A. Erdélyi), ZentralBlatt

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§9.16, 1st item.

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13: Bibliography O

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Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

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Document, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§2.8(iii).

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

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Spectral decomposition of tent maps using symmetry considerations. J. Statist. Phys. 84 (1-2), pp. 269–276.

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ISSN 0022-4715, Document, MathReview (Makoto Mori), ZentralBlatt

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§24.18.

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14: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►A survey is given of the formal spectral theory of second order differential operators, typical results being presented in §1.18(i) through §1.18(viii). … ►One then needs a self-adjoint extension of a symmetric operator to carry out its spectral theory in a mathematically rigorous manner. … ►Spectral expansions of $T$, and of functions $F(T)$ of $T$, these being expansions of $T$ and $F(T)$ in terms of the eigenvalues and eigenfunctions summed over the spectrum, then follow: … ► … ►

Spectral expansions and self-adjoint extensions

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15: Bibliography L

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The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

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In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

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ISSN 0564-6162, Document, MathReview, ZentralBlatt

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§31.18.

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Problems of Mathematical Physics. Revised, enlarged and corrected English edition; translated and edited by Richard A. Silverman. With a supplement by Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..

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Notes:

Republished as Worked Problems in Applied Mathematics by Dover Publications, New York, 1979

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ISBN 0-486-63730-1, MathReview (J. Mathews), ZentralBlatt

Referenced by:

§10.43(v).

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Introduction to spectral theory: selfadjoint ordinary differential operators. Translations of Mathematical Monographs, Vol. 39, American Mathematical Society, Providence, R.I..

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Notes:

Translated from the Russian by Amiel Feinstein

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MathReview Entry

Referenced by:

§1.18(x).

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The spectral analysis of three families of exceptional Laguerre polynomials. J. Approx. Theory 202, pp. 5–41.

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ISSN 0021-9045, Document, Link, MathReview (Edmundo J. Huertas)

Referenced by:

§18.36(vi).

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Linear prediction of bandlimited processes with flat spectral densities. IEEE Trans. Signal Process. 49 (7), pp. 1564–1569.

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ISSN 1053-587X, Document, MathReview, ZentralBlatt

Referenced by:

§30.15(v).

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16: Bibliography

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SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.

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SPHEREPACK 2.0 is a collection of Fortran programs that facilitates computer modeling of geophysical processes. Accurate solutions are obtained via the spectral method that uses both scalar and vector spherical harmonic transforms. The package also contains utility programs for computing the associated Legendre functions. SPHEREPACK 3.1 was released in August 2003.

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FullText, SPHEREPACK 3.1

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1st item.

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Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

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Document, ZentralBlatt

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§11.12.

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Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.

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MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§23.21(ii).

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The classical moment problem and some related questions in analysis. Classics in Applied Mathematics, Vol. 82, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Reprint of the 1965 edition [ 0184042], Translated by N. Kemmer, With a foreword by H. J. Landau

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ISBN 978-1-611976-38-0, MathReview Entry

Referenced by:

§18.40(ii).

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Notes:

Corrected reprint of the 1988 original

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ISBN 0-89871-354-4, MathReview, ZentralBlatt

Referenced by:

§3.7(iii).

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17: Bibliography M

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Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.

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A software package (the successor to CAYLEY) designed to solve computationally hard problems in algebra, number theory, geometry, and combinatorics, and to provide a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric, and geometric objects.

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Magma

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4th item.

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Spectral functions for the Tomonaga-Luttinger model. Phys. Rev. B 46 (24), pp. 15753–15760.

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Document

Referenced by:

§13.28(iii).

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Mathieusche Funktionen und Sphäroidfunktionen mit Anwendungen auf physikalische und technische Probleme. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXI, Springer-Verlag, Berlin (German).

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MathReview (S. C. van Veen), ZentralBlatt

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Table 28.1.1, §28.10(i), §28.11, §28.12(i), §28.12(ii), §28.12(iii), §28.14, §28.15(i), §28.15(ii), §28.16, §28.17, §28.19, §28.2(ii), §28.2(iii), §28.2(iv), §28.2(v), §28.2(vi), §28.20(ii), §28.20(iii), §28.20(vi), §28.20(vii), §28.22(i), §28.22(ii), §28.23, §28.24, §28.25, §28.28(i), 2nd item, 3rd item, §28.33(ii), item (e), item (d), §28.4(i), §28.4(ii), §28.4(iii), §28.4(iv), §28.4(v), §28.4(vi), §28.4(vi), §28.5(i), §28.5(i), §28.6(i), §28.6(ii), §28.7, §28.7, §28.8(i), §28.8(ii), §28.9, Ch.28, §30.1, §30.10, §30.11(iii), §30.11(iii), §30.11(iv), §30.11(v), §30.11(vi), §30.11(vi), §30.13(i), §30.13(ii), §30.13(iii), §30.13(iv), §30.13(v), §30.13(v), §30.14(i), §30.14(ii), §30.14(iii), §30.14(iv), §30.14(v), §30.14(v), §30.16(i), §30.16(i), §30.2(i), §30.2(ii), §30.3(i), §30.3(ii), §30.3(iii), §30.3(iv), §30.4(i), §30.4(ii), §30.4(iv), §30.5, §30.5, §30.6, §30.6, §30.8(i), §30.8(ii), §30.9(i), §30.9(i), §30.9(ii), §30.9(ii), Ch.30, Notations P, Notations P, Notations Q, Notations Q.

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18: Bibliography P

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Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 (6), pp. 1326–1341.

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ISSN 0090-5364, FullText, MathReview (Takeaki Kariya), ZentralBlatt

Referenced by:

§35.9.

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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations. J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.

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Document

Referenced by:

§10.76(ii).

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Numerical Solution of Sturm-Liouville Problems. Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.

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ISBN 0-19-853415-9, MathReview (L. Greenberg), ZentralBlatt

Referenced by:

§3.7(iv).

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