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21: Bibliography F
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  • P. Falloon (2001) Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.
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    Notes:
    Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.
    External Links:
    FullText
    Referenced by:
    §30.12, 1st item, 2nd item.
    Encodings:
    BibTeX
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  • R. H. Farrell (1985) Multivariate Calculation. Use of the Continuous Groups. Springer Series in Statistics, Springer-Verlag, New York.
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    External Links:
    ISBN 0-387-96049-X, MathReview (Yasuko Chikuse), ZentralBlatt
    Referenced by:
    §35.9.
    Encodings:
    BibTeX
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  • K. W. Ford and J. A. Wheeler (1959a) Semiclassical description of scattering. Ann. Physics 7 (3), pp. 259–286.
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    External Links:
    ISSN 0003-4916, Document, MathReview, ZentralBlatt
    Referenced by:
    §9.16.
    Encodings:
    BibTeX
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  • K. W. Ford and J. A. Wheeler (1959b) Application of semiclassical scattering analysis. Ann. Physics 7 (3), pp. 287–322.
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    External Links:
    ISSN 0003-4916, Document, MathReview, ZentralBlatt
    Referenced by:
    §9.16.
    Encodings:
    BibTeX
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  • L. Fox (1960) Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments. National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
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    External Links:
    MathReview (L. J. Slater), ZentralBlatt
    Referenced by:
    3rd item, 2nd item.
    Encodings:
    BibTeX
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    22: Bibliography J
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  • A. T. James (1964) Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.
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  • H. Jeffreys and B. S. Jeffreys (1956) Methods of Mathematical Physics. 3rd edition, Cambridge University Press, Cambridge.
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    Notes:
    Reprinted in 1999.
    External Links:
    MathReview, ZentralBlatt
    Referenced by:
    §10.1, §12.17, Ch.14, Ch.6, §7.18(iv), Ch.9, Notations H, Notations H, Notations K.
    Encodings:
    BibTeX
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  • U. D. Jentschura and E. Lötstedt (2012) Numerical calculation of Bessel, Hankel and Airy functions. Computer Physics Communications 183 (3), pp. 506–519.
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    External Links:
    Document, FullText, ZentralBlatt
    Referenced by:
    §10.19(iii), §10.19(iii).
    Encodings:
    BibTeX
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  • W. R. Johnson (2007) Atomic Structure Theory: Lectures on Atomic Physics. Springer, Berlin and Heidelberg.
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    External Links:
    ISBN 978-3-540-68010-9
    Referenced by:
    §33.22(iv).
    Encodings:
    BibTeX
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    23: 10.73 Physical Applications
    §10.73 Physical Applications
    … β–ΊBessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain. … β–ΊBessel functions of the first kind, J n ⁑ ( x ) , arise naturally in applications having cylindrical symmetry in which the physics is described either by Laplace’s equation ∇ 2 V = 0 , or by the Helmholtz equation ( ∇ 2 + k 2 ) ⁒ ψ = 0 . … β–ΊBessel functions enter in the study of the scattering of light and other electromagnetic radiation, not only from cylindrical surfaces but also in the statistical analysis involved in scattering from rough surfaces. …
    24: Bibliography W
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  • G. Wei and B. E. Eichinger (1993) Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules. Ann. Inst. Statist. Math. 45 (3), pp. 467–475.
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    External Links:
    ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt
    Referenced by:
    §35.9.
    Encodings:
    BibTeX
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  • E. J. Weniger (1989) Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series. Computer Physics Reports 10 (5-6), pp. 189–371.
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    External Links:
    Document
    Referenced by:
    §2.11(vi), §3.9(v), §3.9(vi).
    Encodings:
    BibTeX
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  • E. J. Weniger (1996) Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations. Computers in Physics 10 (5), pp. 496–503.
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    External Links:
    Document
    Referenced by:
    §2.11(vi), §2.11(vi).
    Encodings:
    BibTeX
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  • E. P. Wigner (1959) Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.
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    Notes:
    Expanded and improved ed. Translated from the German by J. J. Griffin.
    External Links:
    ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt
    Referenced by:
    §34.12.
    Encodings:
    BibTeX
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    25: Bibliography H
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  • G. W. Hill (1981) Algorithm 571: Statistics for von Mises’ and Fisher’s distributions of directions: I 1 ⁒ ( x ) / I 0 ⁒ ( x ) , I 1.5 ⁒ ( x ) / I 0.5 ⁒ ( x ) and their inverses [S14]. ACM Trans. Math. Software 7 (2), pp. 233–238.
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    Notes:
    Single-precision Fortran, minimum accuracy 8S.
    External Links:
    ISSN 0098-3500, Document, GAMS (module 571; package TOMS)
    Referenced by:
    5th item.
    Encodings:
    BibTeX
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  • I. D. Hill (1973) Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.
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    Notes:
    Double-precision Fortran, maximum accuracy 12D.
    External Links:
    FullText, Code
    Referenced by:
    5th item.
    Encodings:
    BibTeX
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  • H. Hochstadt (1971) The Functions of Mathematical Physics. Wiley-Interscience [John Wiley & Sons, Inc.], New York-London-Sydney.
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    Notes:
    Pure and Applied Mathematics, Vol. XXIII. Reprinted with corrections by Dover Publications Inc., New York, 1986.
    External Links:
    MathReview, ZentralBlatt
    Referenced by:
    §13.28(i), Ch.13, §15.17(ii), Ch.15.
    Encodings:
    BibTeX
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  • E. Hopf (1934) Mathematical Problems of Radiative Equilibrium. Cambridge Tracts in Mathematics and Mathematical Physics No. 31, Cambridge University Press, Cambridge.
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    Notes:
    Reprinted by Stechert-Hafner, Inc., New York, 1964
    External Links:
    MathReview, ZentralBlatt
    Referenced by:
    §8.19(ix), §8.24(iii).
    Encodings:
    BibTeX
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  • J. Humblet (1984) Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.
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    External Links:
    ISSN 0003-4916, Document, MathReview
    Referenced by:
    §33.10(ii), §33.13, §33.22(vii).
    Encodings:
    BibTeX
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    26: Bibliography R
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  • M. Reed and B. Simon (1975) Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.
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    External Links:
    ISBN 978-0-12-585002-5, MathReview Entry
    Referenced by:
    §1.18(x).
    Encodings:
    BibTeX
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  • M. Reed and B. Simon (1978) Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.
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    External Links:
    ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)
    Referenced by:
    §1.18(x).
    Encodings:
    BibTeX
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  • M. Reed and B. Simon (1979) Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.
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    External Links:
    ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)
    Referenced by:
    §1.18(x).
    Encodings:
    BibTeX
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  • M. Reed and B. Simon (1980) Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis. Elsevier, New York.
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    Notes:
    revised and expanded Edition from 1972,
    External Links:
    ISBN 10: 0-12-585050-6(vol. 1), MathReview Entry
    Referenced by:
    §1.18(x).
    Encodings:
    BibTeX
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  • D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.
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    External Links:
    ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt
    Referenced by:
    §35.9.
    Encodings:
    BibTeX
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    27: Bibliography K
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  • E. L. Kaplan (1948) 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.
    Encodings:
    BibTeX
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  • J. P. Keating (1999) Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In Supersymmetry and Trace Formulae: Chaos and Disorder, J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner (Eds.), pp. 1–15.
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    Referenced by:
    §25.17.
    Encodings:
    BibTeX
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  • C. Kittel (1996) Introduction to Solid State Physics. 7th Edition edition, John Wiley and Sons, New York.
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    External Links:
    ISBN 0-471-11181-3
    Referenced by:
    §1.18(vii).
    Encodings:
    BibTeX
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  • Y. Kivshar and B. Luther-Davies (1998) Dark optical solitons: Physics and applications. Physics Reports 298 (2-3), pp. 81–197.
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    External Links:
    Document
    Referenced by:
    §22.19(iii).
    Encodings:
    BibTeX
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  • Y. A. Kravtsov (1988) Rays and caustics as physical objects. In Progress in Optics, E. Wolf (Ed.), Vol. 26, pp. 227–348.
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    External Links:
    ISBN 0444870962
    Referenced by:
    §36.14(i).
    Encodings:
    BibTeX
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