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1: 10.77 Software

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§10.77(vii) Bessel Functions–Complex Order and Real Argument

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Gil et al. (2014). Fortran.

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Ratnanather et al. (2014). MATLAB.

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2: 14.32 Methods of Computation

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Application of the uniform asymptotic expansions for large values of the parameters given in §§14.15 and 14.20(vii)–14.20(ix).

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For the computation of conical functions see Gil et al. (2009, 2012), and Dunster (2014).

3: Bibliography G

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On high precision methods for computing integrals involving Bessel functions. Math. Comp. 33 (147), pp. 1049–1057.

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External Links:

ISSN 0025-5718, FullText, MathReview (K. Jetter), ZentralBlatt

Referenced by:

§10.74(vii).

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On the generalization of a method for computing Bessel function integrals. J. Comput. Appl. Math. 6 (2), pp. 167–168.

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External Links:

ISSN 0771-050X, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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The triplets of helium. Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.

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External Links:

Document, ZentralBlatt (Möglich, Dr. F.)

Referenced by:

§34.3(vii).

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Matrix Computations. 3rd edition, Johns Hopkins University Press, Baltimore, MD.

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External Links:

ISBN 0-8018-5413-X; 0-8018-5414-8, MathReview, ZentralBlatt

Referenced by:

§3.2(i), §3.2(i), §3.2(ii), §3.2(vii).

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Constructing wavefunctions for nonlocal potentials. J. Chem. Phys. 52, pp. 6211–6217.

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External Links:

Document, MathReview (D. B. Fairlie)

Referenced by:

(9.12.22), (9.12.23), §9.12(vii), §9.17(iii).

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4: 10.74 Methods of Computation

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§10.74(vii) Integrals

… ►For infinite integrals involving products of Bessel functions of the first and second kinds, see Ratnanather et al. (2014). …

5: Bibliography L

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The inhomogeneous Airy functions, $\mathrm{Gi}(z)$ and $\mathrm{Hi}(z)$ . J. Chem. Phys. 72 (1), pp. 332–336.

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External Links:

ISSN 0021-9606, Document, MathReview (V. L. Deshpande)

Referenced by:

(9.12.21), §9.12(vii), §9.17(iii).

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Evaluation of Bessel function integrals with algebraic singularities. J. Comput. Appl. Math. 37 (1-3), pp. 101–112.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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Two index laws for fractional integrals and derivatives. J. Austral. Math. Soc. 14, pp. 385–410.

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External Links:

Document, MathReview (C. Fox), ZentralBlatt

Referenced by:

§1.15(vi), §1.15(vii).

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Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.

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ISSN 0029-599X, Document, MathReview (Vítĕzslav Veselý), ZentralBlatt

Referenced by:

§10.74(vii).

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Integrating some infinite oscillating tails. J. Comput. Appl. Math. 12/13, pp. 109–117.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(vii).

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6: 34.9 Graphical Method

… ►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).

7: Bibliography

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Some orthogonal $q$-polynomials. Math. Nachr. 30, pp. 47–61.

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External Links:

ISSN 0025-584X, Document, MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§18.27(vii).

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Solid State Physics. Holt, Rinehart and Winston, New York.

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External Links:

ISBN 0-03-083993-9

Referenced by:

§1.18(vii), §4.44, §8.22(ii).

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Orthogonal Polynomials and Special Functions. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 21, Society for Industrial and Applied Mathematics, Philadelphia, PA.

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External Links:

ISBN 0-89871-018-9, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(ii), §18.18(vii), Profile Richard A. Askey.

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Continuous $q$-Hermite Polynomials when $q>1$ . In $q$-series and Partitions (Minneapolis, MN, 1988), IMA Vol. Math. Appl., Vol. 18, pp. 151–158.

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External Links:

MathReview (Walter Van Assche), ZentralBlatt

Referenced by:

§18.28(vii).

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Singular Continuous Spectrum for a Class of Almost Periodic Jacobi Matrices. Bulletin of the American Mathematical Society 6 (1), pp. 81–85.

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External Links:

MathReview Entry

Referenced by:

§1.18(vii).

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8: Bibliography W

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The Algebraic Eigenvalue Problem. Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.

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Notes:

Paperback reprint of original edition, published in 1965 by Clarendon Press, Oxford.

External Links:

ISBN 0-19-853418-3, MathReview, ZentralBlatt

Referenced by:

§3.2(v), §3.2(vi), §3.2(vii).

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Computation with Recurrence Relations. Pitman, Boston, MA.

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External Links:

ISBN 0-273-08508-5, MathReview (S. Conde), ZentralBlatt

Referenced by:

§13.29(iv), §16.25, §2.9(iii), §3.10(iii), §3.6(iii), §3.6(v), §3.6(vii).

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On the asymptotic behavior of the Fourier coefficients of Mathieu functions. J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.

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External Links:

ISSN 1044-677X, FullText

Referenced by:

§28.4(vii).

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Quadrature formulas for oscillatory integral transforms. Numer. Math. 39 (3), pp. 351–360.

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ISSN 0029-599X, Document, MathReview (A.J. Rodrigues), ZentralBlatt

Referenced by:

§10.74(vii), §3.5(vii).

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Asymptotic Approximations of Integrals. Academic Press Inc., Boston-New York.

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Notes:

Reprinted with corrections by SIAM, Philadelphia, PA, 2001.

External Links:

ISBN 0-12-762535-6, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§1.14(iv), §1.14(vii), §1.15(iv), §1.16(i), §1.16(ii), §1.16(iii), §1.16(iv), §1.16(v), §1.16(vi), §1.16(vii), §1.16(viii), §14.26, Ch.14, §2.10(iv), §2.3(i), §2.3(ii), §2.3(iii), §2.3(v), §2.4(i), §2.4(ii), §2.4(iv), §2.4(v), §2.4(vi), §2.5(iii), §2.5(i), §2.5(ii), §2.5(ii), §2.5(ii), §2.5(iii), §2.6(iii), §2.6(i), §2.6(i), §2.6(ii), §2.6(ii), §2.6(iii), §2.6(iv), §2.6(iv), Ch.2, §7.20(i), Ch.8, Ch.9, Profile Roderick S. C. Wong.

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9: Bibliography P

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Ideas of Quantum Chemistry. second edition, Elsevier, Amsterdam-New York.

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External Links:

ISBN 978-0-444-59436-5

Referenced by:

§18.39(ii).

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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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External Links:

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

Referenced by:

§10.74(vii).

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A survey of numerical methods for the computation of Bessel function integrals. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 249–265.

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Notes:

International conference on special functions: theory and computation (Turin, 1984)

External Links:

ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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Fourier Series and Integral Transforms. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-59209-7; 0-521-59771-4, MathReview, ZentralBlatt

Referenced by:

§1.14(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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10: Bibliography I

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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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External Links:

ISSN 0044-2267, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§10.74(vii).

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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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Notes:

Proceedings of ENuMath, Santiago de Compostela (2005)

External Links:

ISBN 3-540-34287-7, MathReview, ZentralBlatt

Referenced by:

§3.5(vii).

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$q$-Hermite polynomials, biorthogonal rational functions, and $q$-beta integrals. Trans. Amer. Math. Soc. 346 (1), pp. 63–116.

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ISSN 0002-9947, FullText, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.28(vii).

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Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

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Notes:

With two chapters by Walter Van Assche, With a foreword by Richard A. Askey, Corrected reprint of the 2005 original.

External Links:

ISBN 978-0-521-14347-9, MathReview Entry, ZentralBlatt

Referenced by:

§18.12, (18.15.4_5), (18.16.19), (18.16.20), (18.16.21), §18.17(ii), §18.18(vii), §18.19, (18.2.20), §18.2(vi), §18.2(xii), §18.2(xii), §18.2(x), §18.20(i), §18.20(ii), §18.21(ii), §18.22(i), §18.22(ii), §18.22(iii), §18.23, §18.25(i), §18.25(iii), §18.26(i), §18.26(iv), (18.27.4), §18.27(i), §18.27(ii), §18.27(iii), §18.27(v), §18.27(vi), §18.28(i), §18.28(ii), §18.28(iii), §18.28(v), §18.28(vi), §18.28(vii), §18.28(viii), §18.30(vi), §18.30(vii), §18.30(iii), §18.30(iv), §18.30, §18.30(vi), §18.34(i), §18.34(ii), §18.34(ii), §18.34(iii), (18.35.4), (18.35.5), (18.35.6), (18.35.6_2), (18.35.6_3), (18.35.6_4), (18.35.7), (18.35.8), §18.35(ii), §18.35(iii), §18.36(iii), §18.38(ii), §18.39(iv), §18.39(iv), §18.39(iv), (18.40.4), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

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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.

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External Links:

ISBN 3-528-06355-6, MathReview (Takeshi Sasaki), ZentralBlatt

Referenced by:

§32.2(vi), §32.7(vii).

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