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11: Publications

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Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

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Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007.

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12: 5.10 Continued Fractions

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$a_1=\frac{1}{30},$

… ►For exact values of $a_7$ to $a_{11}$ and 40S values of $a_0$ to $a_{40}$, see Char (1980). …

13: Bibliography K

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Bernstein, Pick, Poisson and related integral expressions for Lambert $W$ . Integral Transforms Spec. Funct. 23 (11), pp. 817–829.

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External Links:

ISSN 1065-2469, Document, Link, MathReview (Ross C. McPhedran), ZentralBlatt

Referenced by:

§4.13.

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Auxiliary table for the incomplete elliptic integrals. J. Math. Physics 27, pp. 11–36.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§19.12.

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Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11 (5), pp. 237–238.

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External Links:

Document, MathReview (C. Gilbert), ZentralBlatt

Referenced by:

§31.17(ii).

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Algorithm 327: Dilogarithm [S22]. Comm. ACM 11 (4), pp. 270–271.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§25.21(v).

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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.

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External Links:

ISSN 1815-0659, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§15.14, §15.14.

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14: Bibliography

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

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Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.

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External Links:

MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§23.21(ii).

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Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Notes:

Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

External Links:

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

Referenced by:

§36.2(i).

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Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.

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External Links:

ISSN 0036-1410, Document, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§17.13, §17.13.

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15: 6.19 Tables

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Abramowitz and Stegun (1964, Chapter 5) includes $x^{-1}\mathrm{Si}\left(x\right)$, $-x^{-2}\mathrm{Cin}\left(x\right)$, $x^{-1}\mathrm{Ein}\left(x\right)$, $-x^{-1}\mathrm{Ein}\left(-x\right)$, $x=0(.01)0.5$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=0.5(.01)2$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x=2(.1)10$; $x\mathrm{f}\left(x\right)$, $x^2\mathrm{g}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x^{-1}=0(.005)0.1$; $\mathrm{Si}\left(\pi x\right)$, $\mathrm{Cin}\left(\pi x\right)$, $x=0(.1)10$. Accuracy varies but is within the range 8S–11S.

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Zhang and Jin (1996, pp. 652, 689) includes $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x=0(.5)20(2)30$, 8D; $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=[0,100]$, 8S.

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Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $E_1\left(z\right)$, $\pm x=0.5,1,3,5,10,15,20,50,100$, $y=0(.5)1(1)5(5)30,50,100$, 8S.

16: 8.26 Tables

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Zhang and Jin (1996, Table 3.8) tabulates $\gamma (a,x)$ for $a=0.5,1,3,5,10,25,50,100$, $x=0(.1)1(1)3,5(5)30,50,100$ to 8D or 8S.

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Pearson (1968) tabulates $I_x(a,b)$ for $x=0.01(.01)1$, $a,b=0.5(.5)11(1)50$, with $b\le a$, to 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

17: 30 Spheroidal Wave Functions

Chapter 30 Spheroidal Wave Functions

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18: Bibliography E

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The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.

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External Links:

Document, ZentralBlatt

Referenced by:

§15.18.

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Further results on McMahon’s asymptotic approximations. J. Phys. A 33 (36), pp. 6333–6341.

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External Links:

ISSN 0305-4470, Document, MathReview (R. G. Aĭrapetyan), ZentralBlatt

Referenced by:

§10.21(vi).

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Higher Transcendental Functions. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, p. 778, v. 30 (1976), no. 135, p. 675, v. 25 (1971), no. 115, p. 635, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 112, p. 999, v. 24 (1970), no. 110, p. 504, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§13.1, §13.10(ii), §13.10(iv), §13.12, §13.13(i), §13.16(ii), §13.16(iii), §13.23(i), §13.23(ii), §13.25, §13.4(i), §13.4(ii), §13.9(i), §13.9(ii), Ch.13, §14.1, §14.10, §14.12(ii), §14.12(i), §14.12(ii), §14.13, §14.13, §14.17(ii), §14.17(iv), §14.18(ii), §14.18(iii), §14.18(iv), §14.19(i), §14.19(ii), §14.19(iii), §14.19(iv), §14.20(v), §14.21(iii), §14.25, §14.28(i), §14.28(ii), §14.3(iii), §14.3(iii), §14.3(iv), §14.5(iii), §14.5(iv), §14.6(i), §14.6(ii), §14.7(iv), §14.8(i), §14.8(ii), Ch.14, §15.16, §15.4(iii), §15.5(i), §15.6, §15.8(v), §15.8(ii), §15.8(v), §15.9(iii), Ch.15, §16.12, §16.12, §16.13, §16.14(i), §16.14(ii), (16.15.3), §16.15, §16.16(i), §16.16(ii), §16.18, §16.20, §16.20, §16.21, §16.4(ii), §16.5, §16.6, Ch.16, §19.21(i), §19.28, §19.5, §24.16(iii), §24.5(i), §24.7(i), §24.7(ii), §24.8(i), Ch.24, (25.11.12), (25.11.18), (25.11.29), (25.11.30), (25.12.12), (25.12.13), (25.14.1), (25.14.4), (25.14.5), (25.14.6), §25.14(i), §25.14(i), §25.14(ii), §25.14(ii), §25.14, (25.5.1), (25.5.10), (25.5.11), (25.5.20), (25.5.21), (25.5.3), (25.5.8), (25.5.9), §25.5(i), §25.5(iii), §25.5, (25.8.5), (25.8.6), §25.8, Ch.25, §5.7(i), Ch.5, Notations P, Notations P, Notations Q.

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Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), (18.17.21_1), §18.17(iv), §18.17(i), §18.17(viii), (18.35.1), (18.35.2), (18.35.4_5), §18.35(i), (18.5.11_1), (18.5.11_3), §18.5(ii), §18.9(iii), §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.

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Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.

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Referenced by:

§25.12(i).

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19: Bibliography F

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Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

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Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

External Links:

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

Referenced by:

3rd item, 2nd item, 1st item.

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Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.

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External Links:

ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt

Referenced by:

§13.3(ii), §15.5(i), §16.3(i).

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On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.

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External Links:

ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.13(i), §32.7(i), §32.7(iii).

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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions. Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.

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External Links:

ISSN 0024-1318, MathReview (D. A. Lutz)

Referenced by:

§32.10(vi).

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Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

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Notes:

Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.

External Links:

ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(ii).

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20: Bibliography Y

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On rational solutions of the second Painlevé equation. Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, pp. 30–35 (Russian).

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Referenced by:

§32.8(ii).

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$L$-squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian. Phys. Rev. A 11 (4), pp. 1144–1156.

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Referenced by:

§18.39(iv), §18.39(iv), §18.39(iv), §18.40(ii).

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