Longman method
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1: 3.5 Quadrature
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►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).
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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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3: Bibliography B
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Asymptotic methods in enumeration.
SIAM Rev. 16 (4), pp. 485–515.
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Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Introduction to Bessel Functions.
Dover Publications Inc., New York.
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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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The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms.
Dover Publications, New York.
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4: Bibliography K
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Numerical Methods and Software.
Prentice Hall, Englewood Cliffs, N.J..
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Separation of Variables for Riemannian Spaces of Constant Curvature.
Longman Scientific & Technical, Harlow.
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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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The Rayleigh function: Theory and computational methods.
Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.
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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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5: Bibliography I
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Ordinary Differential Equations.
Longmans, Green and Co., London.
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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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The method of isomonodromic deformations and relation formulas for the second Painlevé transcendent.
Izv. Akad. Nauk SSSR Ser. Mat. 51 (4), pp. 878–892, 912 (Russian).
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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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Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems.
Vol. 2, Cambridge University Press, Cambridge.
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