F-homotopic%20transformations
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11: 19.36 Methods of Computation
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§19.36(ii) Quadratic Transformations
… ►Computation of Legendre’s integrals of all three kinds by quadratic transformation is described by Cazenave (1969, pp. 128–159, 208–230). ►Quadratic transformations can be applied to compute Bulirsch’s integrals (§19.2(iii)). …The function is computed by descending Landen transformations if is real, or by descending Gauss transformations if is complex (Bulirsch (1965b)). … ►For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20). …12: Bibliography O
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Tables of Lebedev, Mehler and Generalized Mehler Transforms.
Mathematical Note
Technical Report 246, Boeing Scientific Research Lab, Seattle.
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Tables of Fourier Transforms and Fourier Transforms of Distributions.
Springer-Verlag, Berlin.
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Tables of Bessel Transforms.
Springer-Verlag, Berlin-New York.
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Tables of Mellin Transforms.
Springer-Verlag, Berlin-New York.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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13: 8 Incomplete Gamma and Related
Functions
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14: 28 Mathieu Functions and Hill’s Equation
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15: 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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The Laplace Transform: Theory and Applications.
Undergraduate Texts in Mathematics, Springer-Verlag, New York.
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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms.
J. Comput. Phys. 100 (2), pp. 294–296.
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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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16: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Lectures on Integral Transforms.
Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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17: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
18: 23 Weierstrass Elliptic and Modular
Functions
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19: 2.5 Mellin Transform Methods
§2.5 Mellin Transform Methods
… ►The Mellin transform of is defined by …The inversion formula is given by … ► … ►§2.5(iii) Laplace Transforms with Small Parameters
…20: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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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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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
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