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21: Bibliography L

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The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

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Notes:

In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

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ISSN 0564-6162, Document, MathReview, ZentralBlatt

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§31.18.

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The central two-point connection problem for the Heun class of ODEs. J. Phys. A 31 (18), pp. 4249–4261.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

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§31.12.

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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

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ISSN 0010-4655, Document, Code, ZentralBlatt

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4th item.

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A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points. J. Phys. A 19 (3), pp. 329–335.

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ISSN 0305-4470, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.4(vi).

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On the points of inflection of Bessel functions of positive order. I. Canad. J. Math. 42 (5), pp. 933–948.

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Notes:

Corrigenda see same journal, 42(6), p. 1132.

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ISSN 0008-414X, MathReview (A. McD. Mercer), ZentralBlatt

Referenced by:

§10.21(iv).

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22: 32.11 Asymptotic Approximations for Real Variables

… ►with boundary condition … ►If $|k|>1$, then $w_k(x)$ has a pole at a finite point $x=c_0$, dependent on $k$, and … ►and with boundary condition …

23: 2.11 Remainder Terms; Stokes Phenomenon

… ►When a rigorous bound or reliable estimate for the remainder term is unavailable, it is unsafe to judge the accuracy of an asymptotic expansion merely from the numerical rate of decrease of the terms at the point of truncation. … ►Then numerical accuracy will disintegrate as the boundary rays $\mathrm{ph}z=\alpha$, $\mathrm{ph}z=\beta$ are approached. In consequence, practical application needs to be confined to a sector ${\alpha }^{\prime }\le \mathrm{ph}z\le {\beta }^{\prime }$ well within the sector of validity, and independent evaluations carried out on the boundaries for the smallest value of $|z|$ intended to be used. … ►Since the ray $\mathrm{ph}z=\frac{3}{2}\pi$ is well away from the new boundaries, the compound expansion (2.11.7) yields much more accurate results when $\mathrm{ph}z\to \frac{3}{2}\pi$. … ►For large $\rho$ the integrand has a saddle point at $t={\mathrm{e}}^{-\mathrm{i}\theta }$. …

24: Bibliography H

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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

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ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

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On a Painlevé-type boundary-value problem. Quart. J. Mech. Appl. Math. 37 (4), pp. 525–538.

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ISSN 0033-5614, Document, MathReview, ZentralBlatt

Referenced by:

§32.11(i), §32.17.

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The eigenvalues of Mathieu’s equation and their branch points. Stud. Appl. Math. 64 (2), pp. 113–141.

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ISSN 0022-2526, MathReview (R. C. Varma), ZentralBlatt

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§28.7.

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Exponential sums and lattice points. III. Proc. London Math. Soc. (3) 87 (3), pp. 591–609.

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ISSN 0024-6115, Document, Link, MathReview (Angel V. Kumchev), ZentralBlatt

Referenced by:

§27.11, §27.11, Erratum (V1.1.8) for Section 27.11.

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