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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
  • I. M. Longman (1956) Note on a method for computing infinite integrals of oscillatory functions. Proc. Cambridge Philos. Soc. 52 (4), pp. 764–768.
  • 3: Bibliography B
  • E. A. Bender (1974) Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.
  • Å. Björck (1996) Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • F. Bowman (1958) Introduction to Bessel Functions. Dover Publications Inc., New York.
  • P. S. Bullen (1998) A Dictionary of Inequalities. Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 97, Longman, Harlow.
  • W. S. Burnside and A. W. Panton (1960) The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms. Dover Publications, New York.
  • 4: Bibliography K
  • D. K. Kahaner, C. Moler, and S. Nash (1989) Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..
  • E. G. Kalnins (1986) Separation of Variables for Riemannian Spaces of Constant Curvature. Longman Scientific & Technical, Harlow.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • M. K. Kerimov (1999) The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.
  • A. D. Kerr (1978) An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.
  • 5: Bibliography I
  • E. L. Ince (1926) Ordinary Differential Equations. Longmans, Green and Co., London.
  • A. R. Its, A. S. Fokas, and A. A. Kapaev (1994) On the asymptotic analysis of the Painlevé equations via the isomonodromy method. Nonlinearity 7 (5), pp. 1291–1325.
  • A. R. Its and A. A. Kapaev (1987) 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).
  • A. R. Its and V. Yu. Novokshënov (1986) The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.
  • C. Itzykson and J. Drouffe (1989) Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.