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1: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

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The mathematical physics of rainbows and glories. Phys. Rep. 356 (4-5), pp. 229–365 (English).

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External Links:

Document, FullText, ZentralBlatt

Referenced by:

§9.16, §9.16.

Encodings:

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Lectures on Integral Transforms. Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.

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Notes:

Translated from the Russian by H. H. McFaden

External Links:

ISBN 0-8218-4524-1, MathReview, ZentralBlatt

Referenced by:

§10.22(v).

Encodings:

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Mathematical Methods for Physicists. 6th edition, Elsevier, Oxford.

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External Links:

ISBN 0-12-059876-0;0-12-088584-0, MathReview, ZentralBlatt

Referenced by:

§1.17(ii), §1.17(iii).

Encodings:

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Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, New York.

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Notes:

Translated from the 1974 Russian original by K. Vogtmann and A. Weinstein, Corrected reprint of the second (1989) edition

External Links:

ISBN 0-387-96890-3, MathReview

Referenced by:

§21.5(i).

Encodings:

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2: Bibliography B

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

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External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

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Applied Combinatorial Mathematics. Robert E. Krieger, Malabar, FL.

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External Links:

ZentralBlatt

Referenced by:

§26.19, §26.20.

Encodings:

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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.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

Encodings:

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

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

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The SLATEC Common Mathematical Library. In Sources and Development of Mathematical Software, W. R. Cowell (Ed.), pp. 302–320.

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External Links:

GAMS (package SLATEC)

Referenced by:

SLATEC (free Fortran library).

Encodings:

BibTeX

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3: Bibliography S

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Cardinal Spline Interpolation. Society for Industrial and Applied Mathematics, Philadelphia, PA.

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Notes:

Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12

External Links:

MathReview (H. L. Loeb), ZentralBlatt

Referenced by:

§24.17(ii).

Encodings:

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

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

Referenced by:

§28.8(iv).

Encodings:

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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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External Links:

Document

Referenced by:

§22.19(ii).

Encodings:

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

Encodings:

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Orthogonal Polynomials. 3rd edition, American Mathematical Society, New York.

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Notes:

American Mathematical Society Colloquium Publications, Vol. 23

External Links:

MathReview (J. Burlak)

Referenced by:

Ch.14, §9.1, Notations A.

Encodings:

BibTeX

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4: Bibliography M

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

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Hill’s Equation. Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.

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Notes:

Reprinted by Dover Publications, Inc., New York, 1979.

External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§1.3(iii), §28.29(i), §28.29(ii), §28.29(ii), §28.29(iii), §28.29(iii), §28.29(iii), §28.30(i), Ch.28, §29.3(i), §29.9.

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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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External Links:

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

Referenced by:

§10.74(iii).

Encodings:

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

Encodings:

BibTeX

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Methods and Programs for Mathematical Functions. Ellis Horwood Ltd., Chichester.

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Notes:

Includes diskette

External Links:

ISBN 0-13-578998-2, MathReview, ZentralBlatt

Referenced by:

2nd item, CEPHES (free C library).

Encodings:

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5: 7.23 Tables

… ►Lebedev and Fedorova (1960) and Fletcher et al. (1962) give comprehensive indexes of mathematical tables. … ►

Abramowitz and Stegun (1964, Chapter 7) includes $\mathrm{erf}x$, $(2/\sqrt{\pi }){\mathrm{e}}^{-x^2}$, $x\in [0,2]$, 10D; $(2/\sqrt{\pi }){\mathrm{e}}^{-x^2}$, $x\in [2,10]$, 8S; $x{\mathrm{e}}^{x^2}\mathrm{erfc}x$, $x^{-2}\in [0,0.25]$, 7D; $2^n\mathrm{\Gamma }\left(\frac{1}{2}n+1\right){\mathrm{i}}^n\mathrm{erfc}\left(x\right)$, $n=1(1)6,10,11$, $x\in [0,5]$, 6S; $F\left(x\right)$, $x\in [0,2]$, 10D; $xF\left(x\right)$, $x^{-2}\in [0,0.25]$, 9D; $C\left(x\right)$, $S\left(x\right)$, $x\in [0,5]$, 7D; $\mathrm{f}\left(x\right)$, $\mathrm{g}\left(x\right)$, $x\in [0,1]$, $x^{-1}\in [0,1]$, 15D.

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Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of $\mathrm{erf}z$, $x\in [0,5]$, $y=0.5(.5)3$, 7D and 8D, respectively; the real and imaginary parts of ${\int }_x^{\mathrm{\infty }}{\mathrm{e}}^{\pm \mathrm{i}{t}^2}dt$, $(1/\sqrt{\pi }){\mathrm{e}}^{\mp \mathrm{i}(x^2+(\pi /4))}{\int }_x^{\mathrm{\infty }}{\mathrm{e}}^{\pm \mathrm{i}{t}^2}dt$, $x=0(.5)20(1)25$, 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.

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6: Bibliography P

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Zonal Polynomials of Order $1$ Through $12$ . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.

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External Links:

MathReview

Referenced by:

§35.11.

Encodings:

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Evaluation of Fermi-Dirac Integral. In Nonlinear Numerical Methods and Rational Approximation (Wilrijk, 1987), A. Cuyt (Ed.), Mathematics and Its Applications, Vol. 43, pp. 435–444.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

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A new basis for the representation of the rotation group. Lamé and Heun polynomials. J. Mathematical Phys. 14 (8), pp. 1130–1139.

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External Links:

Document, ZentralBlatt

Referenced by:

§29.18(iv).

Encodings:

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

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Gauge Field Theories. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-26537-1, MathReview (G. R. Allcock), ZentralBlatt

Referenced by:

§22.19(ii).

Encodings:

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7: Bibliography F

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Notes:

The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.

External Links:

GAMS (package FDLIBM)

Referenced by:

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

Encodings:

BibTeX

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

Encodings:

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Mathematical Constants. Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-81805-2, MathReview (E. J. Barbeau), ZentralBlatt

Referenced by:

§3.12.

Encodings:

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Basic Hypergeometric Series and Applications. Mathematical Surveys and Monographs, Vol. 27, American Mathematical Society, Providence, RI.

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Notes:

With a foreword by George E. Andrews

External Links:

ISBN 0-8218-1524-5, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.1, §17.16, §17.6(ii), Ch.17, Notations F.

Encodings:

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On weighted polynomial approximation on the whole real axis. Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.

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External Links:

ISSN 0001-5954, Document, Link, MathReview (A. K. Varma)

Referenced by:

§18.32.

Encodings:

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8: Bibliography O

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Tables of Lebedev, Mehler and Generalized Mehler Transforms. Mathematical Note Technical Report 246, Boeing Scientific Research Lab, Seattle.

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Referenced by:

§1.14(viii).

Encodings:

BibTeX

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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

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External Links:

Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

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Bessel Functions. Part III: Zeros and Associated Values. Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.

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External Links:

ISBN 0-521-06153-9, MathReview (L. Fox), ZentralBlatt

Referenced by:

§10.21(vi), §10.21(viii), §10.58, §10.74(vi), 1st item, 2nd item.

Encodings:

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Tables for Bessel Functions of Moderate or Large Orders. National Physical Laboratory Mathematical Tables, Vol. 6. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.

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External Links:

MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§10.20(i), §10.41(ii), 3rd item, 3rd item.

Encodings:

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Applications of Lie Groups to Differential Equations. 2nd edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York.

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External Links:

ISBN 0-387-94007-3; 0-387-95000-1, MathReview, ZentralBlatt

Referenced by:

§32.13(i).

Encodings:

BibTeX

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9: Software Index

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	Open Source													With Book						Commercial
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5.24(ii) $\mathrm{\Gamma }\left(x\right)$, $x\in ℝ$	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	FDLIBM
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20 Theta Functions
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Software published by the journal ACM Transactions on Mathematical Software (TOMS).

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A collection of mathematical software, papers, and databases produced by the numerical analysis research community.

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A cross index of mathematical software in use at NIST.

10: Errata

… ►The following corrections and other changes have been made in the DLMF, and are pending for the Handbook of Mathematical Functions. … ►

Linkage of mathematical symbols to their definitions were corrected or improved.

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Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).

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Bibliographic citations were added in §§1.13(v), 10.14, 10.21(ii), 18.15(v), 18.32, 30.16(iii), 32.13(ii), and as general references in Chapters 19, 20, 22, and 23.

… ►The Handbook of Mathematical Functions was published, and the Digital Library of Mathematical Functions was released.