Weber%20parabolic%20cylinder%20functions

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1: 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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External Links:

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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External Links:

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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2: Bibliography S

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Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electron. Trans. Numer. Anal. 9, pp. 137–146.

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Notes:

Orthogonal polynomials: numerical and symbolic algorithms (Leganés, 1998)

External Links:

ISSN 1068-9613, FullText, MathReview (Adam Marlewski), ZentralBlatt

Referenced by:

§14.30(i), 3rd item.

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On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 3, pp. 226–230.

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ZentralBlatt

Referenced by:

§12.13(i).

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On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series. J. Indian Math. Soc. (N. S.) 4, pp. 34–38.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

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On certain integrals and expansions involving Weber’s parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 4, pp. 158–166.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

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On parabolic cylinder functions. J. Inst. Math. Appl. 4 (1), pp. 106–112.

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Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§12.16.

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3: 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. …

4: Bibliography O

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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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External Links:

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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External Links:

ISSN 0891-6837, MathReview Entry, ZentralBlatt

Referenced by:

§10.29(i), §10.6(i).

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Scattering by a parabolic cylinder—a uniform asymptotic expansion. J. Math. Phys. 26 (4), pp. 854–860.

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ISSN 0022-2488, Document, MathReview (Jean-Louis Guiraud)

Referenced by:

§12.17.

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5: Bibliography F

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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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Notes:

The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.

External Links:

GAMS (package FDLIBM)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

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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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External Links:

MathReview (L. J. Slater), ZentralBlatt

Referenced by:

3rd item, 2nd item.

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On weighted polynomial approximation on the whole real axis. Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.

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ISSN 0001-5954, Document, Link, MathReview (A. K. Varma)

Referenced by:

§18.32.

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6: Bibliography V

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Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Error-Like Functions. CWI Tract, Vol. 10, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam.

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Notes:

A reprint was published in 1986.

External Links:

ISBN 90-6196-277-3, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§5.21, §6.18(iv), §7.22(v), §7.6(i), §7.7(i), §7.7(ii).

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An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

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Transformations of some Gauss hypergeometric functions. J. Comput. Appl. Math. 178 (1-2), pp. 473–487.

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ISSN 0377-0427, Document, Link, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§15.8(v).

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Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.27.

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

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7: Bibliography M

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Tables of Weber Parabolic Cylinder Functions. Her Majesty’s Stationery Office, London.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§10.16, §10.39, §12.14(i), §12.14(ii), §12.14(iv), §12.14(v), §12.14(v), §12.14(vi), §12.14(vii), §12.14(viii), §12.14(x), §12.14(x), 2nd item, §12.2(i), §12.2(ii), §12.2(iii), §12.2(iv), §12.2(v), §12.2(vi), §12.2(vi), §12.4, §12.5(i), §12.5(ii), §12.5(iii), §12.7(i), §12.7(ii), §12.7(iii), §12.7(iii), §12.7(iv), §12.8(i), Ch.12.

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Lie theory and separation of variables. I: Parabolic cylinder coordinates. SIAM J. Math. Anal. 5 (4), pp. 626–643.

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External Links:

Document, MathReview (G. R. Allcock), ZentralBlatt

Referenced by:

§12.13(ii), §12.17.

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Some remarks on zeros of cylinder functions. SIAM J. Math. Anal. 15 (6), pp. 1231–1233.

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ISSN 0036-1410, Document, FullText, MathReview (A. K. Agarwal), ZentralBlatt

Referenced by:

§10.14, §10.21(ii).

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Elastodynamics in parabolic cylinders. Z. Angew. Math. Phys. 39 (5), pp. 748–752.

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ISSN 0044-2275, Document, MathReview (Sergej M. Zverev), ZentralBlatt

Referenced by:

§12.17.

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Tables of the functions of the parabolic cylinder for negative integer parameters. Zastos. Mat. 13, pp. 261–273.

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External Links:

MathReview, ZentralBlatt

Referenced by:

7th item.

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8: Bibliography B

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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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External Links:

Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§12.12.

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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Tables of the Anger and Lommel-Weber Functions. Technical report Technical Report 53 and AFCRL 796, University Washington Press, Seattle.

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Notes:

Reviewed in Math. Comp., v. 17 (1963), pp.315–317.

Referenced by:

1st item.

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The asymptotic analysis of canonical problems in high-frequency scattering theory. II. The circular and parabolic cylinders. Proc. Cambridge Philos. Soc. 74, pp. 313–332.

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External Links:

Document, MathReview (Y. M. Chen)

Referenced by:

§12.17.

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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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External Links:

ISSN 0002-9939, FullText, MathReview, ZentralBlatt

Referenced by:

§12.16.

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