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1—10 of 814 matching pages
1: Bibliography I
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IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017.
The Institute of Electrical and Electronics Engineers, Inc..
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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines.
Z. Angew. Math. Mech. 75 (12), pp. 917–926.
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Highly Oscillatory Quadrature: The Story So Far.
In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.),
pp. 97–118.
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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From Gauss to Painlevé: A Modern Theory of Special Functions.
Aspects of Mathematics E, Vol. 16, Friedr. Vieweg & Sohn, Braunschweig, Germany.
2: Publications
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B. V. Saunders and Q. Wang (2005)
Boundary/Contour Fitted Grid Generation for Effective Visualizations
in a Digital Library of Mathematical Functions,
Proceedings of the 9th International Conference on Numerical Grid Generation
in Computational Field Simulations,
San Jose, June 11–18, 2005. pp. 61–71.
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Q. Wang and B. V. Saunders (2005)
Web-Based 3D Visualization in a Digital Library of Mathematical Functions,
Proceedings of the Web3D Symposium,
Bangor, UK, March 29–April 1, 2005.
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A. Youssef (2007)
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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B. I. Schneider, B. R. Miller and B. V. Saunders (2018)
NIST’s Digital Library of Mathematial Functions,
Physics Today
71, 2, 48 (2018), pp. 48–53.
3: Bibliography K
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Differentialgleichungen: Lösungsmethoden und Lösungen. Teil I.
B. G. Teubner, Stuttgart (German).
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An extension of Saalschütz’s summation theorem for the series
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Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
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Introduction to Solid State Physics.
7th Edition edition, John Wiley and Sons, New York.
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Dualities in the -Askey scheme and degenerate DAHA.
Stud. Appl. Math. 141 (4), pp. 424–473.
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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator.
Adv. Math. 333, pp. 796–821.
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4: Bibliography C
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A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
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Lauricella’s hypergeometric function
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J. Math. Anal. Appl. 7 (3), pp. 452–470.
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Permutation symmetry for theta functions.
J. Math. Anal. Appl. 378 (1), pp. 42–48.
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Optimized fast Hankel transform filters.
Geophysical Prospecting 38 (5), pp. 545–568.
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Properties of generalized Freud polynomials.
J. Approx. Theory 225, pp. 148–175.
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5: 25.21 Software
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§25.21(vii) Fermi–Dirac and Bose–Einstein Integrals
…6: Bibliography R
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The Associated Classical Orthogonal Polynomials.
In Special Functions 2000: Current Perspective and Future
Directions (Tempe, AZ),
NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 255–279.
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Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions.
ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.
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Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis.
Elsevier, New York.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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An extremum property of the -dimensional sphere.
J. Phys. A 13 (10), pp. L349–L351.
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7: 34.9 Graphical Method
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►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 , and symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).
8: 8.28 Software
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§8.28(vii) Generalized Exponential Integral for Complex Argument and/or Parameter
…9: 33.23 Methods of Computation
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►§33.8 supplies continued fractions for and .
Combined with the Wronskians (33.2.12), the values of , , and their derivatives can be extracted.
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►Curtis (1964a, §10) describes the use of series, radial integration, and other methods to generate the tables listed in §33.24.
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§33.23(vii) WKBJ Approximations
… ►Hull and Breit (1959) and Barnett (1981b) give WKBJ approximations for and in the region inside the turning point: .10: 10.74 Methods of Computation
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►In the case of the modified Bessel function see especially Temme (1975).
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►It should be noted, however, that there is a difficulty in evaluating the coefficients , , , and , from the explicit expressions (10.20.10)–(10.20.13) when is close to owing to severe cancellation.
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►Similarly, to maintain stability in the interval the integration direction has to be forwards in the case of and backwards in the case of , with initial values obtained in an analogous manner to those for and .
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►Then and can be generated by either forward or backward recurrence on when , but if then to maintain stability has to be generated by backward recurrence on , and has to be generated by forward recurrence on .
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