Longman method

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1: 3.5 Quadrature

… ►For computing infinite oscillatory integrals, Longman’s method may be used. The integral is written as an alternating series of positive and negative subintegrals that are computed individually; see Longman (1956). …

2: Bibliography L

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Note on a method for computing infinite integrals of oscillatory functions. Proc. Cambridge Philos. Soc. 52 (4), pp. 764–768.

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External Links:

Document, MathReview (D. J. Hofsommer), ZentralBlatt

Referenced by:

§3.5(vii).

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3: Bibliography I

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Ordinary Differential Equations. Longmans, Green and Co., London.

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Notes:

Reprinted by Dover Publications, New York, 1944, 1956.

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.13(i), §1.13(i), §1.13(i), §31.12, §31.14(i), §32.2(i), §32.2(vi), Erratum (V1.0.25) for Section 1.13.

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The factorization method. Rev. Modern Phys. 23 (1), pp. 21–68.

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Referenced by:

§18.38(iii).

Encodings:

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The $J$-matrix method. Adv. in Appl. Math. 46 (1-4), pp. 379–395.

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External Links:

ISSN 0196-8858, Document, Link, MathReview (Boris Petrovich Osilenker)

Referenced by:

§18.39(iv).

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On the asymptotic analysis of the Painlevé equations via the isomonodromy method. Nonlinearity 7 (5), pp. 1291–1325.

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External Links:

ISSN 0951-7715, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.11(iii).

Encodings:

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The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-16483-9, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§32.11(iv), §32.4(i), Profile Alexander A. Its.

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4: Bibliography B

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Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.

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External Links:

Document, MathReview (Bernard Harris), ZentralBlatt

Referenced by:

Ch.2.

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

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Introduction to Bessel Functions. Dover Publications Inc., New York.

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Notes:

Unaltered republication of the 1938 edition, published by Longmans, Green and Co., London-New York.

External Links:

MathReview, ZentralBlatt

Referenced by:

§10.73(iii).

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A Dictionary of Inequalities. Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 97, Longman, Harlow.

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External Links:

ISBN 0-8493-0634-5, MathReview (Lucio Renato Berrone), ZentralBlatt

Referenced by:

§4.18, §4.5(i), §4.5(ii).

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The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms. Dover Publications, New York.

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Notes:

Two volumes. A reproduction of the seventh edition [vol. 1, Longmans, Green, London 1912; vol. 2, Longmans, Green, London 1928].

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.11(i), §1.11(ii), §1.11(iv).

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5: Bibliography K

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Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

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Notes:

Includes collection of single- and double-precision Fortran subroutines.

External Links:

ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

Referenced by:

NMS (free collection of Fortran subroutines).

Encodings:

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Separation of Variables for Riemannian Spaces of Constant Curvature. Longman Scientific & Technical, Harlow.

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External Links:

ISBN 0-582-98807-1, MathReview (H. Kilp), ZentralBlatt

Referenced by:

§31.17(i).

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

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Notes:

Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

External Links:

ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.21(xiii).

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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External Links:

ISSN 0044-2275, Document, MathReview, ZentralBlatt

Referenced by:

§10.71(ii).

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