zeros of cylinder functions

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11: Bibliography B

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Zeros of generalized Airy functions. Mathematika 32 (1), pp. 104–117.

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ISSN 0025-5793, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§9.13(ii).

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Automatic computation of zeros of Bessel functions and other special functions. SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.

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ISSN 1064-8275, Document, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

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A note on integrals involving parabolic cylinder functions. SIAM J. Appl. Math. 16 (1), pp. 71–74.

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Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§12.12.

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Concerning the zeros of some functions related to Bessel functions. J. Mathematical Phys. 10 (9), pp. 1729–1744.

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Document, MathReview (C. V. Coffman), ZentralBlatt

Referenced by:

§10.21(xi).

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Exponential asymptotics for an eigenvalue of a problem involving parabolic cylinder functions. Proc. Amer. Math. Soc. 114 (4), pp. 1025–1032.

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ISSN 0002-9939, FullText, MathReview, ZentralBlatt

Referenced by:

§12.16.

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12: Bibliography O

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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order. Proc. Cambridge Philos. Soc. 47, pp. 699–712.

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Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(vii).

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Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders. J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.

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MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§12.10(i), §12.10(ii), §12.10(iii), §12.10(iv), §12.10(v), §12.10(vii), §12.10(vii), §12.11(iii), §12.11(iii), §12.14(ix), §12.14(ix), §12.14(ix), §12.14(xi), Ch.12, §18.16(v).

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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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ISSN 0308-2105, MathReview (P. F. Hsieh), ZentralBlatt

Referenced by:

§13.20(iii), §13.20(iv).

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Formulae and Tables, The Modified Quotients of Cylinder Functions. Technical report Technical Report UDC 517.564.3:518.25, Vol. 4, Report of the Institute of Industrial Science, University of Tokyo, Institute of Industrial Science, Chiba City, Japan.

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Referenced by:

§10.29(i), §10.6(i).

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Modified quotients of cylinder functions. Math. Tables Aids Comput. 10, pp. 27–28.

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ISSN 0891-6837, MathReview Entry, ZentralBlatt

Referenced by:

§10.29(i), §10.6(i).

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13: Software Index

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	Open Source													With Book						Commercial
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12 Parabolic Cylinder Functions
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

14: Bibliography G

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Integral representations for computing real parabolic cylinder functions. Numer. Math. 98 (1), pp. 105–134.

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ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§12.18.

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Computing the real parabolic cylinder functions $U(a,x)$, $V(a,x)$ . ACM Trans. Math. Software 32 (1), pp. 70–101.

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ISSN 0098-3500, Document, MathReview (Syamal K. Sen), ZentralBlatt

Referenced by:

§12.18.

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Algorithm 850: Real parabolic cylinder functions $U(a,x)$, $V(a,x)$ . ACM Trans. Math. Software 32 (1), pp. 102–112.

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ISSN 0098-3500, Document, MathReview (Syamal K. Sen), ZentralBlatt

Referenced by:

§12.18, 1st item.

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Algorithm 914: parabolic cylinder function $W(a,x)$ and its derivative. ACM Trans. Math. Software 38 (1), pp. Art. 6, 5.

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

Referenced by:

§12.18, §12.18, 2nd item, §12.21(ii).

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Fast and accurate computation of the Weber parabolic cylinder function $W(a,x)$ . IMA J. Numer. Anal. 31 (3), pp. 1194–1216.

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ISSN 0272-4979, Document, FullText, MathReview (Adam Marlewski), ZentralBlatt

Referenced by:

§12.18, §12.18.

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15: Bibliography C

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Determination of $\nu$-zeros of Hankel functions. Comput. Phys. Comm. 32 (3), pp. 333–339.

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Notes:

Double-precision Fortran, maximum accuracy 7S.

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ISSN 0010-4655, Document, Code

Referenced by:

1st item.

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Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

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MathReview (I. I. Hirschman, Jr.), ZentralBlatt

Referenced by:

§12.16.

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The zeros of Hankel functions as functions of their order. Numer. Math. 7 (3), pp. 238–250.

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ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(xiv).

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The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.

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External Links:

MathReview (R. G. Langebartel), ZentralBlatt

Referenced by:

§10.21(x).

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On zeros of the hypergeometric function. Serdica 7 (3), pp. 243–249.

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ISSN 0204-4140, MathReview (R. G. Buschman), ZentralBlatt

Referenced by:

§15.13.

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16: Bibliography I

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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

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ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

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Computing zeros and orders of Bessel functions. J. Comput. Appl. Math. 38 (1-3), pp. 169–184.

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ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

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The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(iii).

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Tables of the elliptic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.

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ZentralBlatt

Referenced by:

4th item, 2nd item.

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Bounds for the small real and purely imaginary zeros of Bessel and related functions. Methods Appl. Anal. 2 (1), pp. 1–21.

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ISSN 1073-2772, FullText, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(v).

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17: Bibliography T

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Parabolic cylinder functions $U(n,x)$ for natural $n$ and positive $x$ . Comput. Phys. Commun. 69, pp. 415–419.

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Notes:

Double-precision Fortran, minimum accuracy 14S, maximum accuracy 21D.

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Document, Code

Referenced by:

4th 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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Asymptotics of zeros of incomplete gamma functions. Ann. Numer. Math. 2 (1-4), pp. 415–423.

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Notes:

Special functions (Torino, 1993)

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ISSN 1021-2655, FullText, MathReview (E. R. Love), ZentralBlatt

Referenced by:

§8.13(ii).

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The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.

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Notes:

Algol procedures, maximum accuracy 14S.

External Links:

FullText, ZentralBlatt

Referenced by:

§12.21(ii).

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Numerical and asymptotic aspects of parabolic cylinder functions. J. Comput. Appl. Math. 121 (1-2), pp. 221–246.

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Notes:

Numerical analysis in the 20th century, Vol. I, Approximation theory

External Links:

ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§12.10(vii), §12.10(vi), §12.10(vi), §12.18.

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18: 32.11 Asymptotic Approximations for Real Variables

… ►where … ►where … ►where … ►Here $U$ denotes the parabolic cylinder function (§12.2). … ►Alternatively, if $\nu$ is not zero or a positive integer, then …

19: Bibliography J

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Some properties of the Erlang loss function. Bell System Tech. J. 53, pp. 525–551.

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ISSN 0005-8580, MathReview (U. Narayan Bhat), ZentralBlatt

Referenced by:

§8.23.

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A note on sampling expansion for a transform with parabolic cylinder kernel. Inform. Sci. 26 (2), pp. 155–158.

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ISSN 0020-0255, Document, MathReview, ZentralBlatt

Referenced by:

§12.16.

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Asymptotic formulas for the zeros of the Meixner polynomials. J. Approx. Theory 96 (2), pp. 281–300.

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ISSN 0021-9045, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§18.24.

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Asymptotics of the hypergeometric function. Math. Methods Appl. Sci. 24 (6), pp. 369–389.

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ISSN 0170-4214, Document, MathReview, ZentralBlatt

Referenced by:

§14.15(iii), §15.12(iii).

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Parabolic cylinder functions of large order. J. Comput. Appl. Math. 190 (1-2), pp. 453–469.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§12.10(vi).

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20: Bibliography F

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On the reversion of an asymptotic expansion and the zeros of the Airy functions. SIAM Rev. 41 (4), pp. 762–773.

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ISSN 1095-7200, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§2.2, §2.2, §3.8(v), §9.9(iv), §9.9(iv).

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Generalized parabolic cylinder functions. Asymptotic Anal. 5 (6), pp. 517–531.

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ISSN 0921-7134, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§12.15.

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Zeros of the Macdonald function of complex order. J. Comput. Appl. Math. 211 (2), pp. 223–231.

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ISSN 0377-0427, Document, FullText, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§10.42, §10.42.

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Complex zeros of the error function and of the complementary error function. Math. Comp. 27 (122), pp. 401–407.

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FullText, MathReview, ZentralBlatt

Referenced by:

§7.13(i), §7.13(ii), 1st item.

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Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments. National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

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MathReview (L. J. Slater), ZentralBlatt

Referenced by:

3rd item, 2nd item.

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