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11: Bibliography N

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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Proofs of two conjectures on the real zeros of the cylinder and Airy functions. SIAM J. Math. Anal. 53 (4), pp. 4328–4349.

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ISSN 0036-1410, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(10.18.17), (10.18.18), §10.18(iii), (9.8.22), (9.8.23), §9.8(iv), Erratum (V1.1.8) for Section 9.8(iv), Erratum (V1.1.8) for Section 10.18(iii).

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A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

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MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

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Hypergeometric functions. Acta Math. 94, pp. 289–349.

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Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§16.10, §16.8(ii), §16.8(ii).

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12: 12.11 Zeros

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§12.11(i) Distribution of Real Zeros

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§12.11(ii) Asymptotic Expansions of Large Zeros

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§12.11(iii) Asymptotic Expansions for Large Parameter

… ►where $t(\zeta )$ is the function inverse to $\zeta (t)$, defined by (12.10.39) (see also (12.10.41)), and … ►For further information, including associated functions, see Olver (1959).

13: 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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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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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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14: Bibliography R

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Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.

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Document

Referenced by:

6th item.

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Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.

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MathReview (H. H. Martens), ZentralBlatt

Referenced by:

§20.11(iv), §20.12(ii).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).

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Link, ISSN 2227-7390, Document

Referenced by:

§8.15.

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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.

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MathReview (J. Shmoys)

Referenced by:

§12.17.

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15: 28.8 Asymptotic Expansions for Large $q$

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§28.8(ii) Sips’ Expansions

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§28.8(iii) Goldstein’s Expansions

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Barrett’s Expansions

… ►The approximants are elementary functions, Airy functions, Bessel functions, and parabolic cylinder functions; compare §2.8. … ►

16: 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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17: 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.

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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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Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

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MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

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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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18: 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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19: Bibliography M

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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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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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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MathReview, ZentralBlatt

Referenced by:

7th item.

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