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11: Bibliography

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Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

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External Links:

Document, ZentralBlatt

Referenced by:

§11.12.

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Some orthogonal $q$-polynomials. Math. Nachr. 30, pp. 47–61.

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External Links:

ISSN 0025-584X, Document, MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§18.27(vii).

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Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

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External Links:

ISBN 0-7923-7119-4, MathReview, ZentralBlatt

Referenced by:

§17.12.

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Note on the trivial zeros of Dirichlet $L$-functions. Proc. Amer. Math. Soc. 94 (1), pp. 29–30.

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ISSN 0002-9939, FullText, MathReview (Jerzy Kaczorowski), ZentralBlatt

Referenced by:

(25.15.7), (25.15.8), §25.15(ii), §25.15.

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Critical points of smooth functions, and their normal forms. Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).

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Notes:

In Russian. English translation: Russian Math. Surveys, 30(1975), no. 5, pp. 1–75.

External Links:

Document, MathReview (D. Siersma), ZentralBlatt

Referenced by:

§36.2(i), Ch.36.

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12: Bibliography T

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LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.

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Notes:

Single-precision Fortran.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

9th item.

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An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives. J. Comput. Phys. 32 (2), pp. 270–279.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.74(vi), §10.77(x).

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The numerical computation of the confluent hypergeometric function $U(a,b,z)$ . Numer. Math. 41 (1), pp. 63–82.

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Notes:

Algol 60 variable-precision procedures are included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§13.29(iv), §13.32(ii).

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Über die Lamésche Differentialgleichung. Math. Nachr. 30, pp. 137–154 (German).

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External Links:

Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§29.18(iv).

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13: 29.21 Tables

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Arscott and Khabaza (1962) tabulates the coefficients of the polynomials $P$ in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues $h$ for $k^2=0.1(.1)0.9$, $n=1(1)30$. Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.

14: 31.18 Methods of Computation

… ►The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.

15: Peter A. Clarkson

… ► Kruskal), J. Math. Phys., 30 (1989) 2201–2213. …

16: Hans Volkmer

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30 Spheroidal Wave Functions

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17: Bibliography F

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Computation of complex Airy functions and their zeros using asymptotics and the differential equation. ACM Trans. Math. Software 30 (4), pp. 471–490.

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External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt

Referenced by:

§9.17(ii), §9.17(v), §9.8(iv).

Encodings:

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Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

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Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

External Links:

ISSN 0098-3500, Document, Code, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, 2nd item, 1st item.

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The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

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ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

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Complex roots of $\sin z=az$, $\cos z=az$, and $\cosh z=az$ . Math. Comp. 30 (135), pp. 541–545.

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FullText, MathReview (Gerhard Merz), ZentralBlatt

Referenced by:

§4.46.

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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions. Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.

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External Links:

ISSN 0024-1318, MathReview (D. A. Lutz)

Referenced by:

§32.10(vi).

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18: 24.1 Special Notation

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$B_2=\frac{1}{30}$ ,

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$B_4=\frac{1}{30},\mathrm{\dots }$ .

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19: 24.20 Tables

… ►Wagstaff (1978) gives complete prime factorizations of $N_n$ and $E_n$ for $n=20(2)60$ and $n=8(2)42$, respectively. In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, respectively. …

20: Bibliography S

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Ein Verfahren zur Berechnung des charakteristischen Exponenten der Mathieuschen Differentialgleichung I. Numer. Math. 3 (1), pp. 30–38.

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External Links:

ISSN 0029-599X, Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

item (b).

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Sharper bounds for the Chebyshev functions $\theta (x)$ and $\psi (x)$. II. Math. Comp. 30 (134), pp. 337–360.

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Notes:

For corrigendum see same journal v. 30 (1976), no. 136, p. 900

External Links:

FullText, Document, MathReview (R. P. Brent), ZentralBlatt

Referenced by:

§27.12.

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Confluent Hypergeometric Functions. Cambridge University Press, Cambridge-New York.

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Notes:

Table errata: Math. Comp. v. 30 (1976), no. 135, 677–678

External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§13.1, §13.10(ii), §13.10(iii), (13.11.3), §13.11, §13.13(i), §13.13(ii), §13.13(iii), §13.14(i), §13.14(vi), §13.15(i), §13.15(ii), §13.16(ii), §13.16(iii), §13.2(v), §13.2(vi), §13.21(i), §13.23(i), §13.24, §13.26(i), §13.26(ii), §13.26(iii), §13.3(i), §13.3(ii), 2nd item, §13.4(i), §13.4(ii), §13.8(i), §13.9(i), §13.9(ii), Ch.13, §8.5.

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Structure of avoided crossings for eigenvalues related to equations of Heun’s class. J. Phys. A 30 (2), pp. 673–687.

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ISSN 0305-4470, Document, MathReview (Éric Delabaere), ZentralBlatt

Referenced by:

§31.13.

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Effective calculation of the incomplete gamma function for parameter values $\alpha =(2n+1)/2$, $n=0,\mathrm{\dots },5$ . Angew. Informatik 17, pp. 30–32.

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Notes:

Includes Fortran code.

External Links:

ZentralBlatt

Referenced by:

§8.28(ii).

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