distributional%20methods

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1: Bibliography P

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Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.

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ISSN 1364-5021, Document, MathReview (F. Ursell), ZentralBlatt

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§10.20(ii).

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Handbook of the Normal Distribution. Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.

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Notes:

A revised and expanded 2nd edition was published in 1996.

External Links:

ISBN 0-8247-1541-1, MathReview (S. Kotz), ZentralBlatt

Referenced by:

§7.20(iii).

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The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt

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§35.9.

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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.

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ISSN 0010-4655, Document, Code

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6th item.

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A method for computing Bessel function integrals. J. Comput. Phys. 75 (2), pp. 334–344.

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ISSN 0021-9991, Document, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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2: 3.8 Nonlinear Equations

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Bisection Method

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Secant Method

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Eigenvalue Methods

… ►For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013). … ►

3: Bibliography K

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Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

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Notes:

Includes collection of single- and double-precision Fortran subroutines.

External Links:

ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

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NMS (free collection of Fortran subroutines).

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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Document, MathReview (Matti Jutila), ZentralBlatt

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§25.18(i).

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The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

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Notes:

Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

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ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.21(xiii).

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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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Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).

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Notes:

In cooperation with W. Rudert

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MathReview, ZentralBlatt

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1st item.

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4: Bibliography C

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Ellipsoidal distributions of charge or mass. J. Mathematical Phys. 2, pp. 441–450.

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MathReview (H. Bremekamp), ZentralBlatt

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§19.33(iv), §19.37(iv).

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Algorithm AS 310. Computing the non-central beta distribution function. Appl. Statist. 46 (1), pp. 146–156.

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Notes:

Single-precision Fortran.

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FullText, Code, ZentralBlatt

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2nd item.

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Calculation of angular distributions in complex angular momentum theories of elastic scattering. Molecular Physics 37 (6), pp. 1703–1712.

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Document

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§14.31(iii).

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Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34 (4), pp. 1270–1285.

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FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.4(i), §35.4(ii).

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Methods of mathematical physics. Vol. I. Interscience Publishers, Inc., New York, N.Y..

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External Links:

MathReview (J. B. Diaz), ZentralBlatt

Referenced by:

(14.30.8_5).

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5: 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.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

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Geometrical and Catastrophe Optics Methods in Scattering. In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.), Vol. 21, pp. 1–234.

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§36.14(ii).

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Numerical Methods for Roots of Polynomials. Part I. Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.

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ISBN 978-0-444-52729-5; 0-444-52729-X, MathReview Entry, ZentralBlatt

Referenced by:

§3.8(iv).

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The exponential integral distribution. Statist. Probab. Lett. 5 (3), pp. 209–211.

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ISSN 0167-7152, Document, MathReview Entry, ZentralBlatt

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§8.19(xi).

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

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Notes:

Includes diskette

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

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2nd item, CEPHES (free C library).

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6: Bibliography S

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A global Newton method for the zeros of cylinder functions. Numer. Algorithms 18 (3-4), pp. 259–276.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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

Referenced by:

§28.8(iv).

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Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

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ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

Referenced by:

§3.9(vi).

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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).

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A Guide to Distribution Theory and Fourier Transforms. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.

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ISBN 0-8493-8273-4, MathReview (J. Horváth), ZentralBlatt

Referenced by:

§18.17(v).

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7: Bibliography W

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The distribution of the zeros of Jacobian elliptic functions with respect to the parameter $k$ . Comput. Methods Funct. Theory 9 (2), pp. 579–591.

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ISSN 1617-9447, MathReview (M. K. Jain), ZentralBlatt

Referenced by:

§22.4(i).

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Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.

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Document, ZentralBlatt

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§33.5(ii).

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The generalised product moment distribution in samples from a normal multivariate population. Biometrika 20A, pp. 32–52.

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FullText, Document, ZentralBlatt

Referenced by:

§35.3(i), §35.3(ii).

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The method of Darboux. J. Approximation Theory 10 (2), pp. 159–171.

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Document, MathReview (M. E. Noble), ZentralBlatt

Referenced by:

§2.10(iv).

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On a uniform treatment of Darboux’s method. Constr. Approx. 21 (2), pp. 225–255.

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ISSN 0176-4276, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(iv).

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8: 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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On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (4), pp. 1119–1178.

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ISSN 0894-0347, FullText, MathReview (David J. Aldous), ZentralBlatt

Referenced by:

§32.14.

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Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.

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External Links:

Document

Referenced by:

§24.18.

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Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.

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Document, MathReview (Bernard Harris), ZentralBlatt

Referenced by:

Ch.2.

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Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis. J. Multivariate Anal. 41 (2), pp. 314–337.

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ISSN 0047-259X, Document, MathReview (A. L. Rukhin), ZentralBlatt

Referenced by:

§35.10, §35.9.

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9: Bibliography O

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Tables of Fourier Transforms and Fourier Transforms of Distributions. Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-50630-6; 0-387-50630-6, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §10.22(vi), §10.43(vi), §11.10(x), §11.7(v), §11.9(iv), §12.12, §13.10(iv), §13.23(ii), §18.17(ix), §6.14(iii), §7.14(iii).

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On the distribution of spacings between zeros of the zeta function. Math. Comp. 48 (177), pp. 273–308.

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ISSN 0025-5718, FullText, Author’s Website, MathReview (S. L. Segal), ZentralBlatt

Referenced by:

§25.18(ii).

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Asymptotic Enumeration Methods. In Handbook of Combinatorics, Vol. 2, L. Lovász, R. L. Graham, and M. Grötschel (Eds.), pp. 1063–1229.

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External Links:

ISBN 0-444-82351-4, Pdf, MathReview (Konrad Engel), ZentralBlatt

Referenced by:

Ch.2.

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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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Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

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Distribution of the partition function modulo $m$ . Ann. of Math. (2) 151 (1), pp. 293–307.

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ISSN 0003-486X, FullText, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§27.14(v).

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10: 1.11 Zeros of Polynomials

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§1.11(ii) Elementary Properties

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$z_1{z}_2\mathrm{\cdots }{z}_n={(-1)}^n{a}_0/a_n.$

… ►For another method see §4.43. … ►Resolvent cubic is $z^3+12z^2+20z+9=0$ with roots ${\theta }_1=-1$, ${\theta }_2=-\frac{1}{2}(11+\sqrt{85})$, ${\theta }_3=-\frac{1}{2}(11-\sqrt{85})$, and $\sqrt{-{\theta }_1}=1$, $\sqrt{-{\theta }_2}=\frac{1}{2}(\sqrt{17}+\sqrt{5})$, $\sqrt{-{\theta }_3}=\frac{1}{2}(\sqrt{17}-\sqrt{5})$. …