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21: 34.9 Graphical Method

§34.9 Graphical Method

►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …For an account of this method see Brink and Satchler (1993, Chapter VII). For specific examples of the graphical method of representing sums involving the $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).

22: 20 Theta Functions

Chapter 20 Theta Functions

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23: Bibliography I

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The factorization method. Rev. Modern Phys. 23 (1), pp. 21–68.

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§18.38(iii).

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The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

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§24.12(i).

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The $J$-matrix method. Adv. in Appl. Math. 46 (1-4), pp. 379–395.

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ISSN 0196-8858, Document, Link, MathReview (Boris Petrovich Osilenker)

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§18.39(iv).

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On the asymptotic analysis of the Painlevé equations via the isomonodromy method. Nonlinearity 7 (5), pp. 1291–1325.

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ISSN 0951-7715, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

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§32.11(iii).

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The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.

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ISBN 3-540-16483-9, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§32.11(iv), §32.4(i), Profile Alexander A. Its.

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24: Publications

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Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007.

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Tensor Product B-Spline Mesh Generation for Accurate Surface Visualizations in the NIST Digital Library of Mathematical Functions, in Mathematical Methods for Curves and Surfaces, Proceedings of the 2008 International Conference on Mathematical Methods for Curves and Surfaces (MMCS 2008), Lecture Notes in Computer Science, Vol. 5862, (M. Dæhlen, M. Floater., T. Lyche, J. L. Merrien, K. Mørken, L. L. Schumaker, eds), Springer, Berlin, Heidelberg (2010) pp. 385–393.

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NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53.

25: 17.18 Methods of Computation

§17.18 Methods of Computation

… ►Method (2) is very powerful when applicable (Andrews (1976, Chapter 5)); however, it is applicable only rarely. Lehner (1941) uses Method (2) in connection with the Rogers–Ramanujan identities. ►Method (1) can sometimes be improved by application of convergence acceleration procedures; see §3.9. Shanks (1955) applies such methods in several $q$-series problems; see Andrews et al. (1986).

26: 12.18 Methods of Computation

§12.18 Methods of Computation

►Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs. …

27: Bibliography N

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Modern Computing Methods. 2nd edition, Notes on Applied Science, No. 16, Her Majesty’s Stationery Office, London.

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MathReview (A. S. Householder), ZentralBlatt

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§3.8(iv).

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

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§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

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§19.37(iv).

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An explicit formula for the coefficients in Laplace’s method. Constr. Approx. 38 (3), pp. 471–487.

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ISSN 0176-4276, Document, Link, MathReview (Pedro J. Pagola), ZentralBlatt

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§5.11(i), §5.11(i).

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An extension of Laplace’s method. Constr. Approx. 51 (2), pp. 247–272.

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ISSN 0176-4276, Document, Link, MathReview (José Luis López), ZentralBlatt

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(11.11.16), (11.11.17), §11.11(iii).

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28: 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

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§10.71(ii).

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On some boundary element methods for the heat equation. Numer. Math. 46 (1), pp. 101–120.

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ISSN 0029-599X, Document, MathReview (Reinhard Scholz), ZentralBlatt

Referenced by:

§7.8.

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29: Bibliography O

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

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Ch.2.

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Computing $\pi (x)$: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.

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Notes:

Online fulltext contains postpublication annotations.

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FullText

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§27.18.

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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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A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.

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Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(ii).

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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order. Proc. Cambridge Philos. Soc. 47, pp. 699–712.

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Document, MathReview (J. Todd), ZentralBlatt

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§10.21(vii).

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30: Bibliography R

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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).

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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

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ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.

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ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis. Elsevier, New York.

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revised and expanded Edition from 1972,

External Links:

ISBN 10: 0-12-585050-6(vol. 1), MathReview Entry

Referenced by:

§1.18(x).

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General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

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Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

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