parabolic%20cylinder%20functions

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11: Bibliography L

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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

Referenced by:

§4.13, 2nd item, §4.48(iv).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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Functions on a parabolic cylinder with a negative integer index. Differ. Uravn. 21 (11), pp. 2001–2003, 2024 (Russian).

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Notes:

In Russian.

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ISSN 0374-0641, MathReview, ZentralBlatt

Referenced by:

§12.13(i).

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Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

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ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

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Integral representation of the Hankel function in terms of parabolic cylinder functions. Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.

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Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§12.12, §12.16.

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12: Bibliography B

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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

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Notes:

Double-precision Fortran code.

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Document, Code

Referenced by:

1st item, 4th 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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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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ISSN 0002-9939, FullText, MathReview, ZentralBlatt

Referenced by:

§12.16.

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13: 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.

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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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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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14: 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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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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