turning points

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11: Bibliography O

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Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

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Document, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§2.8(iii).

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Second-order linear differential equations with two turning points. Philos. Trans. Roy. Soc. London Ser. A 278, pp. 137–174.

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FullText, MathReview (P. F. Hsieh), ZentralBlatt

Referenced by:

§2.8(vi).

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Improved error bounds for second-order differential equations with two turning points. J. Res. Nat. Bur. Standards Sect. B 80B (4), pp. 437–440.

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MathReview (Peter Deuflhard), ZentralBlatt

Referenced by:

§2.8(vi).

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Connection formulas for second-order differential equations with multiple turning points. SIAM J. Math. Anal. 8 (1), pp. 127–154.

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Document, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

§2.8(v), (9.13.13), (9.13.17), §9.13(i), §9.13(i).

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Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities. SIAM J. Math. Anal. 8 (4), pp. 673–700.

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Document, MathReview (W. Wasow), ZentralBlatt

Referenced by:

§2.8(v).

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12: 2.9 Difference Equations

… ►For discussions of turning points, transition points, and uniform asymptotic expansions for solutions of linear difference equations of the second order see Wang and Wong (2003, 2005). …

13: 2.8 Differential Equations with a Parameter

… ►Zeros of $f(z)$ are also called turning points. … ►

§2.8(iii) Case II: Simple Turning Point

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§2.8(v) Multiple and Fractional Turning Points

►The approach used in preceding subsections for equation (2.8.1) also succeeds when $z_0$ is a multiple or fractional turning point. … ►For two coalescing turning points see Olver (1975a, 1976) and Dunster (1996a); in this case the uniform approximants are parabolic cylinder functions. …

14: Bibliography D

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Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point. SIAM J. Math. Anal. 21 (6), pp. 1594–1618.

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.26, §2.8(vi).

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Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane. SIAM J. Math. Anal. 25 (2), pp. 322–353.

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ISSN 0036-1410, Document, MathReview (H. C. Howard), ZentralBlatt

Referenced by:

§2.8(vi).

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Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Proc. Roy. Soc. London Ser. A 452, pp. 1331–1349.

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ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.8(vi), §8.12, §8.12.

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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

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ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

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15: 33.22 Particle Scattering and Atomic and Molecular Spectra

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§33.22(vi) Solutions Inside the Turning Point

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16: Bibliography P

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On the computation of zeros and turning points of Bessel functions. Bull. Soc. Math. Grèce (N.S.) 31, pp. 117–122.

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MathReview (Alan M. Cohen), ZentralBlatt

Referenced by:

§10.76(ii).

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Approximation for the turning points of Bessel functions. J. Comput. Phys. 64 (1), pp. 253–257.

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ISSN 0021-9991, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.76(ii).

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17: Bibliography W

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

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Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

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ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

Ch.9.

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18: Bibliography N

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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole. Ph.D. Thesis, University of Maryland, College Park, MD.

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Referenced by:

§2.8(vi).

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19: Bibliography G

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WKB and turning point theory for second-order difference equations. In Spectral Methods for Operators of Mathematical Physics, Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.

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FullText, MathReview (Ioannis K. Purnaras), ZentralBlatt

Referenced by:

§18.15(v), §18.15(v).

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Computing the zeros and turning points of solutions of second order homogeneous linear ODEs. SIAM J. Numer. Anal. 41 (3), pp. 827–855.

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ISSN 0036-1429, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi), §3.8(v).

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20: Bibliography B

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Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

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ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.8(iii).

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Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions. SIAM J. Math. Anal. 17 (2), pp. 422–450.

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.15(iv), §14.15(iv), §14.26, §2.8(vi).

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Asymptotic expansions for the coefficient functions that arise in turning-point problems. Proc. Roy. Soc. London Ser. A 410, pp. 35–60.

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ISSN 0080-4630, FullText, MathReview (P. F. Hsieh), ZentralBlatt

Referenced by:

§2.8(iii).

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