Gram%E2%80%93Schmidt%20procedure

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21: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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Document

Referenced by:

§33.22(iv).

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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

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1st item, 4th item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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Document, ZentralBlatt

Referenced by:

§10.73(iv).

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Methods of calculation of radial wave functions and new tables of Coulomb functions. Physical Rev. (2) 80, pp. 553–560.

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Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§33.7.

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Numerical calculation of the sine, cosine and Fresnel integrals. Numer. Math. 9 (5), pp. 380–385.

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Notes:

Algol 60 procedures for sine, cosine, and 2 Fresnel integrals are included.

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

Referenced by:

2nd item, §7.25(iv).

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22: 10.34 Analytic Continuation

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23: 12.12 Integrals

… ►For compendia of integrals see Erdélyi et al. (1953b, v. 2, pp. 121–122), Erdélyi et al. (1954a, b, v. 1, pp. 60–61, 115, 210–211, and 336; v. 2, pp. 76–80, 115, 151, 171, and 395–398), Gradshteyn and Ryzhik (2000, §7.7), Magnus et al. (1966, pp. 330–331), Marichev (1983, pp. 190–191), Oberhettinger (1974, pp. 144–145), Oberhettinger (1990, pp. 106–108 and 192), Oberhettinger and Badii (1973, pp. 181–185), Prudnikov et al. (1986b, pp. 36–37, 155–168, 243–246, 289–290, 327–328, 419–420, and 619), Prudnikov et al. (1992a, §3.11), and Prudnikov et al. (1992b, §3.11). …

24: 19.37 Tables

… ►Tabulated for $\varphi =5^{\circ }(5^{\circ }){80}^{\circ }({2.5}^{\circ }){90}^{\circ }$, ${\alpha }^2=-1(.1)-0.1,0.1(.1)1$, $k^2=0(.05)0.9(.02)1$ to 10D by Fettis and Caslin (1964) (and warns of inaccuracies in Selfridge and Maxfield (1958) and Paxton and Rollin (1959)). …

25: Bibliography C

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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

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ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt

Referenced by:

§16.24(ii).

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Orthogonalization Procedures and the Localization of Wannier Functions. Phys. Rev. 105, pp. 102–103.

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Document, Link, ZentralBlatt

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Profile Bille C. Carlson.

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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

Referenced by:

§13.29(v), §15.19(v).

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Inverse Acoustic and Electromagnetic Scattering Theory. 2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.

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ISBN 3-540-62838-X, MathReview, ZentralBlatt

Referenced by:

§10.73(i).

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26: Hans Volkmer

… ►Subsequently, he spent eleven years at the University of Essen as an assistant to Professor Dieter Schmidt, and then in 1990 joined the faculty at the University of Wisconsin–Milwaukee. …

27: Bibliography J

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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.

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ISSN 0167-2789, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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Modifications of Coulombic interactions by polarizable atoms. Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.

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ISSN 0305-0041, Document, MathReview (Cataldo Agostinelli)

Referenced by:

§34.12.

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28: 18.5 Explicit Representations

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$T_5\left(x\right)=16x^5-20x^3+5x,$

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$U_6\left(x\right)=64x^6-80x^4+24x^2-1.$

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$L_6\left(x\right)=\frac{1}{720}{x}^6-\frac{1}{20}{x}^5+\frac{5}{8}{x}^4-\frac{10}{3}{x}^3+\frac{15}{2}{x}^2-6x+1.$

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29: Bibliography L

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Elliptic Functions and Applications. Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.

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ISBN 0-387-96965-9, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.2(ii), §19.36(iii), §20.13, §20.15, §20.2(i), §20.2(ii), §20.2(iii), §20.2(iv), §20.4(i), §20.5(i), §20.5(ii), §20.7(i), §20.7(ii), §20.7(iv), §20.7(vi), §20.7(vii), §20.7(vii), §20.7(viii), Ch.20, §22.10(i), §22.10(ii), §22.12, §22.13(i), §22.14(i), §22.14(ii), §22.14(iii), §22.14(iii), §22.15(i), §22.15(ii), §22.15(ii), §22.16(ii), §22.16(iii), §22.17(i), §22.18(i), §22.18(iii), §22.19(ii), §22.19(i), §22.19(i), §22.19(ii), §22.19(ii), §22.19(iv), §22.19(v), §22.2, §22.20(vii), §22.21, §22.4(i), §22.4(iii), §22.5(i), §22.5(ii), §22.6(ii), §22.6(iii), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), §22.8(ii), Ch.22, §23.10(i), §23.10(i), §23.10(iii), §23.10(iv), §23.12, §23.2(ii), §23.2(iii), §23.2(iii), §23.21(i), §23.3(i), §23.3(ii), §23.6(iv), §23.6(i), §23.6(i), §23.6(ii), §23.6(ii), §23.6(iii), §23.7, §23.8(i), §23.8(ii), §23.8(iii), Ch.23.

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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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30: 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.

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ISSN 0010-4655, Document, Code

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9th item.

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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.

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

Referenced by:

§13.29(iv), §13.32(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.

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FullText, ZentralBlatt

Referenced by:

§12.21(ii).

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