harmonic analysis

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11: Bibliography B

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NJGRAF: An efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM. Comput. Phys. Comm. 50 (3), pp. 375–393.

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1st item.

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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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The asymptotic analysis of canonical problems in high-frequency scattering theory. II. The circular and parabolic cylinders. Proc. Cambridge Philos. Soc. 74, pp. 313–332.

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Document, MathReview (Y. M. Chen)

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§12.17.

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Associated Legendre polynomials, ordinary and modified spherical harmonics. Comput. Phys. Comm. 5 (5), pp. 390–394.

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Single-precision Fortran, maximum accuracy 16S

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2nd item.

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Two cold atoms in a harmonic trap. Found. Phys. 28 (4), pp. 549–559.

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Document

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§12.17.

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12: Bibliography

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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.

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MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

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The classical moment problem and some related questions in analysis. Classics in Applied Mathematics, Vol. 82, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Reprint of the 1965 edition [ 0184042], Translated by N. Kemmer, With a foreword by H. J. Landau

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ISBN 978-1-611976-38-0, MathReview Entry

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§18.40(ii).

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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

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Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

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1st item.

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A harmonic mean inequality for the gamma function. J. Comput. Appl. Math. 87 (2), pp. 195–198.

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Notes:

For corrigendum see same journal v. 90 (1998), no. 2, p. 265

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

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§5.6(i).

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$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. CBMS Regional Conference Series in Mathematics, Vol. 66, Amer. Math. Soc., Providence, RI.

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ISBN 0-8218-0716-1, MathReview (David M. Bressoud), ZentralBlatt

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§17.14, §17.14, §17.16, Ch.17, Profile George E. Andrews.

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13: Bibliography G

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A harmonic mean inequality for the gamma function. SIAM J. Math. Anal. 5 (2), pp. 278–281.

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Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§5.6(i).

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A code to evaluate prolate and oblate spheroidal harmonics. Comput. Phys. Comm. 108 (2-3), pp. 267–278.

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Double-precision Fortran, maximum accuracy 18S

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Document, Code, ZentralBlatt

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5th item, 1st item.

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Evaluation of toroidal harmonics. Comput. Phys. Comm. 124 (1), pp. 104–122.

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4th item.

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DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics. Comput. Phys. Comm. 139 (2), pp. 186–191.

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2nd item.

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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. J. Phys. A 47 (1), pp. 015203, 26 pp..

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ISSN 1751-8113, Document, Link, MathReview (Brian Simanek)

Referenced by:

§18.36(vi), §18.36(vi).

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14: Bibliography D

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Introduction to Vector Analysis. 5th edition, Allyn and Bacon Inc., Boston, MA.

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Notes:

Seventh edition printed by WCB/McGraw-Hill, 1995.

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ISBN 0-697-06356-9; 0-697-16099-8, MathReview (R. H. Bowman), ZentralBlatt

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§1.5(ii).

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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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The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.

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Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

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On the computation of Mathieu functions. J. Engrg. Math. 7, pp. 39–61.

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Notes:

Variable-precision Algol program, maximum precision 15D

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Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§28.36(ii), §28.36(iii).

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Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comput. Appl. Math. 80 (1), pp. 127–161.

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ISSN 0377-0427, Document, MathReview (Eberhard Wagner), ZentralBlatt

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§2.11(iii), §8.20(ii).

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15: Bibliography C

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On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.

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Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§34.12.

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Landen Transformations of Integrals. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 75–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.22(iii).

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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A dispersion analysis for difference schemes: Tables of generalized Airy functions. Math. Comp. 32 (144), pp. 1163–1170.

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ISSN 0025-5718, FullText, MathReview (Philip Brenner), ZentralBlatt

Referenced by:

§9.13(ii).

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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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16: 18.38 Mathematical Applications

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§18.38(i) Classical OP’s: Numerical Analysis

… ►Light and Carrington Jr. (2000) review and extend the one-dimensional analysis to solution of multi-dimensional many-particle systems, where the sparse nature of the resulting matrices is highly advantageous. …Each of these typically require a particular non-classical weight functions and analysis of the corresponding OP’s. … ►

Zonal Spherical Harmonics

►Ultraspherical polynomials are zonal spherical harmonics. …