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11: Bibliography S

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The elliptical microstrip antenna with circular polarization. IEEE Trans. Antennas and Propagation 29 (1), pp. 90–94.

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5th item.

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Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.

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Document

Referenced by:

§22.19(ii).

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

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A new Fortran program for the $9$-$j$ angular momentum coefficient. Comput. Phys. Comm. 56 (2), pp. 231–248.

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Document, ZentralBlatt

Referenced by:

§34.13.

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An extension of Airy’s equation. SIAM J. Appl. Math. 15 (6), pp. 1400–1412.

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Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

(9.13.1), (9.13.10), (9.13.11), (9.13.12), (9.13.2), (9.13.3), (9.13.4), (9.13.5), (9.13.6), (9.13.7), (9.13.8), (9.13.9), §9.13(i), §9.13(i).

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12: Bibliography H

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Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.

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

Referenced by:

§29.16.

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On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.

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FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§9.13(i).

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An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.

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ZentralBlatt

Referenced by:

§24.6.

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On the higher-order Stokes phenomenon. Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.

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ISSN 1364-5021, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§2.11(iv).

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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order. Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.

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ISSN 1364-5021, Document, MathReview (A. D. Wood), ZentralBlatt

Referenced by:

§10.20(ii).

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13: Bibliography G

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A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp. 21 (97), pp. 18–29.

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FullText, MathReview (D. C. Gilles), ZentralBlatt

Referenced by:

§10.74(v), §3.10(ii).

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Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions. ACM Trans. Math. Software 28 (3), pp. 325–336.

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Notes:

Double-precision Fortran, maximum accuracy 18S.

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ISSN 0098-3500, Document, GAMS (module 819; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

3rd item.

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Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions. ACM Trans. Math. Software 28 (4), pp. 436–447.

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Notes:

Double-precision Fortran, maximum accuracy 18S.

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ISSN 0098-3500, Document, GAMS (module 822; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

2nd item.

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GNU Scientific Library The GNU Project.

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Notes:

The GNU Scientific Library is a large general purpose numerical software library with broad coverage of elementary and special functions. Implementation is in double precision.

External Links:

Home Page

Referenced by:

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

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General approach to few-cycle intense laser interactions with complex atoms. Phys. Rev. A 76, pp. 053411.

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External Links:

Document, Link

Referenced by:

§3.2(vi).

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14: Bibliography T

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Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.

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ISSN 0044-2267, Document, MathReview (B. C. Carlson), ZentralBlatt

Referenced by:

§22.11.

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Computational aspects of incomplete gamma functions with large complex parameters. In Approximation and Computation. A Festschrift in Honor of Walter Gautschi, R. V. M. Zahar (Ed.), International Series of Numerical Mathematics, Vol. 119, pp. 551–562.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§8.11(iii), §8.20(ii), §8.25(i), §8.25(iii), 2nd item, 3rd item.

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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations. Phys. Rev. Lett. 29 (16), pp. 1114–1118.

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External Links:

Document

Referenced by:

§31.17(ii).

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Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners. John Wiley & Sons Inc., New York.

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Notes:

With CD-ROM containing a large collection of mathematical function software written in Fortran 90 and Mathematica (an edition with the same software in C and Mathematica exists also). The functions are computed for real variables only. Maximum accuracy 12D.

External Links:

ISBN 0-471-18171-4, MathReview, ZentralBlatt

Referenced by:

§19.36(ii), § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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Une nouvelle représentation explicite des nombres d’Euler. C. R. Acad. Sci. Paris Sér. A-B 286 (19), pp. A807–A809.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§24.6.

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15: Bibliography F

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Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.

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ISSN 0219-5305, Document, Link, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§15.12(iii), §15.12(iii).

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The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

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ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

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Incomplete gamma functions for large values of their variables. Adv. in Appl. Math. 34 (3), pp. 467–485.

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ISSN 0196-8858, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§8.12.

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The second Appell function for one large variable. Mediterr. J. Math. 10 (4), pp. 1853–1865.

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ISSN 1660-5446, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

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Uniform asymptotic expansions of certain classes of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.

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External Links:

Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§16.22.

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16: Bibliography M

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Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd edition, Springer-Verlag, New York-Berlin.

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Notes:

Table errata: Math. Comp. v. 23 (1969), p. 471, v. 24 (1970), pp. 240 and 505, v. 25 (1971), no. 113, p. 201, v. 29 (1975), no. 130, p. 672, v. 30 (1976), no. 135, pp. 677–678, v. 32 (1978), no. 141, pp. 319–320, v. 36 (1981), no. 153, pp. 315–317, v. 41 (1983), no. 164, pp. 775–776, and v. 81 (2012), no. 280, p. 2251

External Links:

MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.15, §10.22(vi), §10.32(iv), §10.38, §10.43(vi), §10.60(iv), §10.9(iv), §11.5(iii), Ch.11, §12.12, §12.5(iv), Ch.12, §13.10(vi), §13.23(iv), §14.1, §14.11, §14.12(ii), §14.18(iv), §14.25, §14.3(iii), §14.5(v), §14.7(iv), Ch.14, (25.5.21), §25.5, (25.6.1), (25.6.2), §25.6(i), §8.1, Notations B, Notations I, Notations P, Notations P, Notations Q, Notations Q.

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Painlevé functions of the third kind. J. Mathematical Phys. 18 (5), pp. 1058–1092.

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External Links:

ISSN 0022-2488, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§32.11(iv), §32.16, §32.16, §32.16, §32.2(iii).

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The zeros of $a{z}^2{J}_{\nu }^{\prime \prime }(z)+bz{J}_{\nu }^{\prime }(z)+c{J}_{\nu }(z)$ as functions of order. Internat. J. Math. Math. Sci. 15 (2), pp. 319–322.

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ISSN 0161-1712, Document, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(iv).

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An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York.

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ISBN 0-471-58884-9, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§1.15(vi), Erratum (V1.0.14) for Subsections 1.15(vi), 1.15(vii), 2.6(iii).

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Stirling numbers of the second kind. Duke Math. J. 25 (1), pp. 29–43.

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External Links:

Document, MathReview (A. Sade), ZentralBlatt

Referenced by:

§26.1, §26.8(vii), Notations S.

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BibTeX

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17: Bibliography K

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A proof of the $q$-Macdonald-Morris conjecture for $B{C}_n$ . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.

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External Links:

ISSN 0065-9266, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§17.14.

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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ISSN 0044-2275, Document, MathReview, ZentralBlatt

Referenced by:

§10.71(ii).

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Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters. J. B. Wolters, Groningen.

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External Links:

MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.11(iii).

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Zeros of exceptional Hermite polynomials. J. Approx. Theory 200, pp. 28–39.

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External Links:

ISSN 0021-9045, Document, Link, MathReview (Mario Pérez Riera)

Referenced by:

§18.39(i).

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18: Errata

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17.6.1 $${}_2{}^{}\varphi _1^{}(\genfrac{}{}{0pt}{}{a,b}{c};q,c/(ab))=\frac{{(c/a,c/b;q)}_{\mathrm{\infty }}}{{(c,c/(ab);q)}_{\mathrm{\infty }}},$$

The constraint was added.

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18.28.2 $${\int }_{-1}^1{p}_n(x)p_m(x)w(x)dx=h_n{\delta }_{n,m},$$ $|a|,|b|,|c|,|d|\le 1$, $ab,ac,ad,bc,bd,cd\ne 1$

The constraint of this equation was updated to include $ab,ac,ad,bc,bd,cd\ne 1$.

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An entire new Subsection 13.8(iv) “Large $a$ and $b$”, was added.

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Version 1.0.9 (August 29, 2014)

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Version 1.0.3 (Aug 29, 2011)

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19: Bibliography

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High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder. J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.

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FullText

Referenced by:

§36.14(ii).

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Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

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Algorithms for special integrals of ordinary differential equations. J. Phys. A 29 (5), pp. 973–991.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§32.10(i).

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Study of nuclear structure by electromagnetic excitation with accelerated ions. Rev. Mod. Phys. 28, pp. 432–542.

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External Links:

ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§33.22(ii).

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20: Bibliography L

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A Numerical Library in C for Scientists and Engineers. CRC Press, Boca Raton, FL.

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Notes:

With 1 IBM-PC floppy disk (3.5 inch; HD) containing a large general purpose mathematical software collection written in C including a collection of special function classes. The functions are computed for real variables only. (See Lau (2004) for Java version).

External Links:

ISBN 0-8493-7376-X, MathReview, ZentralBlatt

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, H. T. Lau (2004).

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A Numerical Library in Java for Scientists & Engineers. Chapman & Hall/CRC, Boca Raton, FL.

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Notes:

With 1 CD-ROM (Windows, Macintosh and Unix) containing a large general purpose mathematical software collection written in Java including a collection of special function classes. The functions are computed for real variables only. (See Lau (1995) for C version).

External Links:

ISBN 1-58488-430-4, MathReview Entry, ZentralBlatt

Referenced by:

H. T. Lau (1995).

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Eine Verallgemeinerung der Sphäroidfunktionen. Arch. Math. 11, pp. 29–39.

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ISSN 0003-9268, Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§30.12.

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The confluent hypergeometric functions $M(a,b;z)$ and $U(a,b;z)$ for large $b$ and $z$ . J. Comput. Appl. Math. 233 (6), pp. 1570–1576.

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External Links:

ISSN 0377-0427, Document, FullText, MathReview, ZentralBlatt

Referenced by:

§13.8(ii), §13.8(ii).

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Large degree asymptotics of generalized Bernoulli and Euler polynomials. J. Math. Anal. Appl. 363 (1), pp. 197–208.

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External Links:

ISSN 0022-247X, Document, Link, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§24.16(i), §24.16(i).

Encodings:

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