Levin%20transformations
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
►§1.14(i) Fourier Transform
… ►§1.14(iii) Laplace Transform
… ►Fourier Transform
… ►Laplace Transform
…2: 3.9 Acceleration of Convergence
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§3.9(i) Sequence Transformations
… ►§3.9(iv) Shanks’ Transformation
… ►§3.9(v) Levin’s and Weniger’s Transformations
►We give a special form of Levin’s transformation in which the sequence of partial sums is transformed into: …Sequences that are accelerated by Levin’s transformation include logarithmically convergent sequences, i. …3: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Orthogonal Polynomials for Exponential Weights.
CMS Books in Mathematics/Ouvrages de Mathématiques de la
SMC, 4, Springer-Verlag, New York.
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Orthogonal polynomials for exponential weights on
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J. Approx. Theory 134 (2), pp. 199–256.
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Algorithm 344: Student’s t-distribution [S14].
Comm. ACM 12 (1), pp. 37–38.
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On the theory of diffraction by an aperture in an infinite plane screen. I.
Phys. Rev. 74 (8), pp. 958–974.
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4: 2.11 Remainder Terms; Stokes Phenomenon
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►shows that this direct estimate is correct to almost 3D.
►The fourth column of Table 2.11.1 gives the results of applying the following variant of Levin’s transformation:
…For example, using double precision is found to agree with (2.11.31) to 13D.
►However, direct numerical transformations need to be used with care.
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5: 11.12 Physical Applications
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►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)).
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6: 18.32 OP’s with Respect to Freud Weights
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►However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986).
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►For (generalized) Freud weights on a subinterval of see also Levin and Lubinsky (2005).
7: 20 Theta Functions
Chapter 20 Theta Functions
…8: 8.28 Software
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►See also Dorrer (1968), Gautschi (1964a), Hill (1970), Levine (1969), Morris (1969), and Phien (1990).
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9: 20.10 Integrals
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§20.10(i) Mellin Transforms with respect to the Lattice Parameter
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20.10.1
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20.10.2
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20.10.3
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§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
…10: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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