divergent%20integrals
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5 matching pages
1: 22.3 Graphics
2: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Non-linear transformations of divergent and slowly convergent sequences.
J. Math. Phys. 34, pp. 1–42.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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3: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series.
Chelsea Publishing Co., New York.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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4: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Some useful integrals of
and related integrals.
Optica Acta 14 (3), pp. 317–322.
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Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series.
Computer Physics Reports 10 (5-6), pp. 189–371.
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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations.
Computers in Physics 10 (5), pp. 496–503.
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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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5: 2.11 Remainder Terms; Stokes Phenomenon
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►For divergent expansions the situation is even more difficult.
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►As an example consider
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►However, regardless whether we can bound the remainder, the accuracy achievable by direct numerical summation of a divergent asymptotic series is always limited.
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►The transformations in §3.9 for summing slowly convergent series can also be very effective when applied to divergent asymptotic series.
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►For example, using double precision is found to agree with (2.11.31) to 13D.
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