asymptotic%20approximations
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1: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
… βΊLastly, the function in (12.10.3) and (12.10.4) has the asymptotic expansion: … βΊThe proof of the double asymptotic property then follows with the aid of error bounds; compare §10.41(iv). … βΊ2: 2.11 Remainder Terms; Stokes Phenomenon
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§2.11(i) Numerical Use of Asymptotic Expansions
… βΊ … βΊ§2.11(ii) Connection Formulas
… βΊ§2.11(iii) Exponentially-Improved Expansions
… βΊ§2.11(vi) Direct Numerical Transformations
…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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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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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 V
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Rational approximations for exponential integrals
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Acad. Roy. Belg. Bull. Cl. Sci. (5) 56, pp. 1064–1072.
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Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
J. Math. Anal. Appl. 269 (1), pp. 317–331.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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5: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Asymptotic approximations for prolate spheroidal wave functions.
Studies in Appl. Math. 54 (4), pp. 315–349.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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A continued fraction approximation of the gamma function.
J. Math. Anal. Appl. 402 (2), pp. 405–410.
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6: Bibliography C
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Asymptotic approximations for symmetric elliptic integrals.
SIAM J. Math. Anal. 25 (2), pp. 288–303.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Introduction to Approximation Theory.
2nd edition, Chelsea Publishing Co., New York.
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Chebyshev approximations for the Fresnel integrals.
Math. Comp. 22 (102), pp. 450–453.
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Rational Chebyshev approximations for the error function.
Math. Comp. 23 (107), pp. 631–637.
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7: 11.6 Asymptotic Expansions
§11.6 Asymptotic Expansions
βΊ§11.6(i) Large , Fixed
… βΊMore fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions (§2.1(v)). … βΊand for an estimate of the relative error in this approximation see Watson (1944, p. 336).8: 28.8 Asymptotic Expansions for Large
§28.8 Asymptotic Expansions for Large
… βΊBarrett’s Expansions
… βΊDunster’s Approximations
βΊDunster (1994a) supplies uniform asymptotic approximations for numerically satisfactory pairs of solutions of Mathieu’s equation (28.2.1). … βΊ9: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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The Bounds for the Error Term of an Asymptotic Approximation of Jacobi Polynomials.
In Orthogonal Polynomials and Their Applications (Segovia, 1986),
Lecture Notes in Math., Vol. 1329, pp. 203–221.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents.
Methods Appl. Anal. 2 (4), pp. 475–489.
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