distributional methods

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11: 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

Referenced by:

§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

Referenced by:

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

Referenced by:

§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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MathReview (J. B. Diaz), ZentralBlatt

Referenced by:

(14.30.8_5).

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12: Philip J. Davis

… ►Davis joined the Section as part of a distinguished group of researchers studying mathematical methods for exploiting the new computational power. … ►He also had a big influence on the development of the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (A&S), which became one of the most widely distributed and highly cited publications in NIST’s history. … ►In 1961, Davis hired Frank W. J. Olver, a founding member of the Mathematics Division and Head of the Numerical Methods Section at the National Physical Laboratory, Teddington, U. …

13: Bibliography L

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Computing $\pi (x)$: The Meissel-Lehmer method. Math. Comp. 44 (170), pp. 537–560.

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ISSN 0025-5718, FullText, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§27.18.

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An efficient derivative-free method for solving nonlinear equations. ACM Trans. Math. Software 11 (3), pp. 250–262.

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Notes:

Corrigendum, ibid. 15(3) (1989), 287

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ISSN 0098-3500, Document, MathReview (T. Feagin), ZentralBlatt

Referenced by:

§3.8(iii).

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Algorithm 344: Student’s t-distribution [S14]. Comm. ACM 12 (1), pp. 37–38.

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Notes:

Single-precision Fortran, maximum accuracy 8S. For Remarks see same journal 13(1970), pp. 124 and 449.

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ISSN 0001-0782, Document, Remark 1 and Remark 2

Referenced by:

§8.28(iv).

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Sur la distribution des nombres premiers. Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

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ZentralBlatt

Referenced by:

§27.12.

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Note on a method for computing infinite integrals of oscillatory functions. Proc. Cambridge Philos. Soc. 52 (4), pp. 764–768.

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Document, MathReview (D. J. Hofsommer), ZentralBlatt

Referenced by:

§3.5(vii).

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14: Bibliography T

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Asymptotic inversion of the incomplete beta function. J. Comput. Appl. Math. 41 (1-2), pp. 145–157.

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Asymptotic methods in analysis and combinatorics

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ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

§8.18(ii).

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Asymptotic Methods for Integrals. Series in Analysis, Vol. 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.

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ISBN 978-981-4612-15-9, MathReview Entry, ZentralBlatt

Referenced by:

§12.9(i), §12.9(i), (13.8.13), (13.8.14), (13.8.15), (13.8.16), §13.8(ii), §13.8(ii), §13.8(iii), §13.8(iii), §14.15(i), §14.15(i), §14.15(iii), §14.15(iii), §15.12(iii), §15.12(iii), §18.15(vi), §18.15(vi), §2.4(v), §2.4(v), §2.4(vi), §2.4(vi), §26.8(vii), §26.8(vii), §33.12(i), §33.12(i), §33.12(ii), §33.12(ii), Profile Nico M. Temme.

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Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1), pp. 151–174.

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ISSN 0010-3616, FullText, MathReview (Estelle L. Basor), ZentralBlatt

Referenced by:

§32.14.

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Iterative Methods for the Solution of Equations. Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..

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MathReview (W. C. Rheinboldt), ZentralBlatt

Referenced by:

§3.8(iii).

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Some methods for flows past blunt slender bodies. J. Fluid Mech. 18, pp. 619–635.

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ISSN 0022-1120, Document, MathReview (L. E. Payne)

Referenced by:

§18.17(viii).

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15: 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

Referenced by:

§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.

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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

Referenced by:

§35.9.

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Modified Clenshaw-Curtis method for the computation of Bessel function integrals. BIT 23 (3), pp. 370–381.

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ISSN 0006-3835, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(vii).

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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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16: Bibliography Z

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Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach. Ann. Numer. Math. 2 (1-4), pp. 457–472.

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ISSN 1021-2655, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§13.9(i), §15.13.

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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.

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Notes:

Reprint of 1965 McGraw-Hill Publication

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ISBN 0-486-65479-6, MathReview Entry

Referenced by:

§1.16(ix).

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A note on the $\tau$-method approximations for the Bessel functions $Y_0(z)$ and $Y_1(z)$ . Comput. Math. Appl. 31 (9), pp. 63–70.

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ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§10.76(ii).

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17: Bibliography B

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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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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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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

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18: Bibliography J

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Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.

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FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.11, §35.4(i), §35.4(ii), §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35.

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Bounds on Dawson’s integral occurring in the analysis of a line distribution network for electric vehicles. Eurandom Preprint Series Technical Report 14, Eurandom, Eindhoven, The Netherlands.

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Notes:

ISSN 1389-2355

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FullText

Referenced by:

§7.8, §7.8.

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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.

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Continuous Univariate Distributions. 2nd edition, Vol. I, John Wiley & Sons Inc., New York.

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ISBN 0-471-58495-9, MathReview (D. N. Shanbhag), ZentralBlatt

Referenced by:

§7.20(iii), §8.23.

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Continuous Univariate Distributions. 2nd edition, Vol. II, John Wiley & Sons Inc., New York.

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ISBN 0-471-58494-0, MathReview (D. N. Shanbhag), ZentralBlatt

Referenced by:

§8.23.

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19: Errata

… ►It was decided that much more information should be given in the section on general OP’s, and as a consequence Chapter 1 (Algebraic and Analytic Methods), also required a significant expansion. … ►We have also completely expanded our discussion on applications of orthogonal polynomials in the physical sciences, and also methods of computation for orthogonal polynomials. … ►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions. … ►

Several changes have been made to

1. make consistent use of the Fourier transform notations $ℱ\left(f\right)$, $ℱ\left(\varphi \right)$ and $ℱ\left(u\right)$ where $f$ is a function of one real variable, $\varphi$ is a test function of $n$ variables associated with tempered distributions, and $u$ is a tempered distribution (see (1.14.1), (1.16.29) and (1.16.35));

2. introduce the partial differential operator $𝐃$ in (1.16.30);

3. clarify the definition (1.16.32) of the partial differential operator $P(𝐃)$; and

4. clarify the use of $P(𝐃)$ and $P(𝐱)$ in (1.16.33), (1.16.34), (1.16.36) and (1.16.37).

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An entire new Subsection 1.16(viii) Fourier Transforms of Special Distributions, was contributed by Roderick Wong.

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20: Bibliography D

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Methods of Numerical Integration. 2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.

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External Links:

ISBN 0-12-206360-0, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§3.5(iii), §3.5(i), §3.5(i), §3.5(ii), §3.5(iii), §3.5(iv), §3.5(v), §3.5(vi), §3.5(vii), §3.5(x).

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Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§2.2, Ch.2, §26.7(iv), §26.7(iv), §4.13.

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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes. Phys. Rev. E (3) 57 (1), pp. 252–275.

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ISSN 1063-651X, Document, MathReview (Victor I. Stepanov), ZentralBlatt

Referenced by:

§31.17(ii).

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The computation of lattice frequency distribution functions by means of continued fractions. Physica 39 (3), pp. 413–423.

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ISSN 0031-8914, Document, Link

Referenced by:

§18.40(ii).

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Algorithm 322. F-distribution. Comm. ACM 11 (2), pp. 116–117.

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Notes:

Includes Algol program, maximum accuracy 10S. For certification see same journal 12(1969), p. 39

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ISSN 0001-0782, Document

Referenced by:

§8.28(iv).

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