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11: Bibliography W
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  • Z. Wang and R. Wong (2006) Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. J. Math. Pures Appl. (9) 85 (5), pp. 698–718.
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    External Links:
    ISSN 0021-7824, Document, MathReview (Rabah Khaldi), ZentralBlatt
    Referenced by:
    §18.29.
    Encodings:
    BibTeX
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  • E. J. Weniger (2007) Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.
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    External Links:
    ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt
    Referenced by:
    §2.10(i).
    Encodings:
    BibTeX
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  • R. Wong and Y.-Q. Zhao (2003) Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials. Anal. Appl. (Singap.) 1 (2), pp. 213–241.
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    External Links:
    ISSN 0219-5305, Document, MathReview (Eberhard Wagner), ZentralBlatt
    Referenced by:
    §18.15(i), §18.15(i).
    Encodings:
    BibTeX
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  • R. Wong and Y. Zhao (2004) Uniform asymptotic expansion of the Jacobi polynomials in a complex domain. Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.
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    External Links:
    ISSN 1364-5021, Document, MathReview (Pet”r Rusev), ZentralBlatt
    Referenced by:
    §18.15(i).
    Encodings:
    BibTeX
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  • R. Wong (1973b) On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.
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    External Links:
    Document, MathReview (L. Berg), ZentralBlatt
    Referenced by:
    §8.11(v).
    Encodings:
    BibTeX
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    12: Bibliography O
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  • A. B. Olde Daalhuis (1998c) On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. Methods Appl. Anal. 5 (4), pp. 425–438.
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    External Links:
    ISSN 1073-2772, Pdf, MathReview (Éric Delabaere), ZentralBlatt
    Referenced by:
    §8.12.
    Encodings:
    BibTeX
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  • A. B. Olde Daalhuis (2000) On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles. Methods Appl. Anal. 7 (4), pp. 727–745.
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    External Links:
    ISSN 1073-2772, Pdf, MathReview (Raimundas Vidunas), ZentralBlatt
    Referenced by:
    §36.12(iii).
    Encodings:
    BibTeX
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  • A. B. Olde Daalhuis (2003a) Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.
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    External Links:
    ISSN 0219-5305, Document, MathReview, ZentralBlatt
    Referenced by:
    §15.12(iii).
    Encodings:
    BibTeX
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  • F. W. J. Olver (1980a) Asymptotic approximations and error bounds. SIAM Rev. 22 (2), pp. 188–203.
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    External Links:
    ISSN 0036-1445, Document, MathReview (L. Berg), ZentralBlatt
    Referenced by:
    §2.7(iii).
    Encodings:
    BibTeX
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  • F. W. J. Olver (1980b) Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
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    External Links:
    ISSN 0308-2105, MathReview (P. F. Hsieh), ZentralBlatt
    Referenced by:
    §13.20(iii), §13.20(iv).
    Encodings:
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    13: Bibliography B
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  • A. P. Bassom, P. A. Clarkson, C. K. Law, and J. B. McLeod (1998) Application of uniform asymptotics to the second Painlevé transcendent. Arch. Rational Mech. Anal. 143 (3), pp. 241–271.
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    External Links:
    ISSN 0945-8396, Document, MathReview (Andrei A. Kapaev), ZentralBlatt
    Referenced by:
    §32.11(ii).
    Encodings:
    BibTeX
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  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
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    External Links:
    Document, ZentralBlatt
    Referenced by:
    §36.14(iii), §9.16.
    Encodings:
    BibTeX
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  • M. V. Berry (1969) Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.
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    Referenced by:
    §36.14(i), §9.16.
    Encodings:
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  • M. V. Berry (1989) Uniform asymptotic smoothing of Stokes’s discontinuities. Proc. Roy. Soc. London Ser. A 422, pp. 7–21.
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    External Links:
    ISSN 0080-4630, FullText, MathReview (André Hautot), ZentralBlatt
    Referenced by:
    §2.11(iv).
    Encodings:
    BibTeX
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  • R. Bo and R. Wong (1994) Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.
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    External Links:
    ISSN 1073-2772, Pdf, MathReview (Eberhard Wagner), ZentralBlatt
    Referenced by:
    §18.24.
    Encodings:
    BibTeX
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    14: Bibliography P
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  • B. V. Pal′tsev (1999) On two-sided estimates, uniform with respect to the real argument and index, for modified Bessel functions. Mat. Zametki 65 (5), pp. 681–692 (Russian).
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    Notes:
    English translation in Math. Notes 65 (1999) pp. 571-581.
    External Links:
    ISSN 0025-567X, Document, MathReview (Boro Döring), ZentralBlatt
    Referenced by:
    §10.37.
    Encodings:
    BibTeX
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  • R. B. Paris (2002a) Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.
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    External Links:
    ISSN 0377-0427, Document, MathReview, ZentralBlatt
    Referenced by:
    §8.12.
    Encodings:
    BibTeX
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  • R. B. Paris (2002b) A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.
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  • R. Piessens (1982) Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.
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    Notes:
    Double-precision Fortran, maximum accuracy 20S.
    External Links:
    ISSN 0010-4655, Document, Code
    Referenced by:
    6th item.
    Encodings:
    BibTeX
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  • R. Piessens (1984a) Chebyshev series approximations for the zeros of the Bessel functions. J. Comput. Phys. 53 (1), pp. 188–192.
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    External Links:
    ISSN 0021-9991, Document, MathReview (Walter Gautschi), ZentralBlatt
    Referenced by:
    §10.76(ii).
    Encodings:
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    15: 18.40 Methods of Computation
    … β–ΊUsually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. … β–ΊThese quadrature weights and abscissas will then allow construction of a convergent sequence of approximations to w ⁑ ( x ) , as will be considered in the following paragraphs. … β–Ί
    Stieltjes Inversion via (approximate) Analytic Continuation
    … β–ΊResults of low ( 2 to 3 decimal digits) precision for w ⁑ ( x ) are easily obtained for N ∼ 10 to 20 . … β–ΊIn Figure 18.40.2 the approximations were carried out with a precision of 50 decimal digits.
    16: 2.11 Remainder Terms; Stokes Phenomenon
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    §2.11(i) Numerical Use of Asymptotic Expansions
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    §2.11(ii) Connection Formulas
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    §2.11(iii) Exponentially-Improved Expansions
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    §2.11(vi) Direct Numerical Transformations
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    17: Bibliography M
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  • A. J. MacLeod (1996b) Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.
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    Notes:
    Includes Fortran code, maximum accuracy 20S.
    External Links:
    ISSN 1017-1398, Document, MathReview, ZentralBlatt
    Referenced by:
    §6.13, 4th item, §6.21(ii).
    Encodings:
    BibTeX
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  • F. Matta and A. Reichel (1971) Uniform computation of the error function and other related functions. Math. Comp. 25 (114), pp. 339–344.
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    External Links:
    FullText, MathReview, ZentralBlatt
    Referenced by:
    §7.22(i).
    Encodings:
    BibTeX
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  • J. W. Miles (1975) Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.
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    External Links:
    MathReview (M. L. Mehta), ZentralBlatt
    Referenced by:
    §30.9(i).
    Encodings:
    BibTeX
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  • D. S. Moak (1981) The q -analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.
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    External Links:
    ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt
    Referenced by:
    §18.27(v).
    Encodings:
    BibTeX
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  • C. Mortici (2013a) A continued fraction approximation of the gamma function. J. Math. Anal. Appl. 402 (2), pp. 405–410.
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    External Links:
    ISSN 0022-247X, Document, FullText, MathReview (Paul Levrie), ZentralBlatt
    Referenced by:
    §5.10.
    Encodings:
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