products%20of%20Bessel%20functions

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11: Bibliography C

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Remarks on the zeros of cross-product Bessel functions. J. Soc. Indust. Appl. Math. 12 (3), pp. 580–587.

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External Links:

Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§10.21(x), §10.21(x).

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The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.

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External Links:

MathReview (R. G. Langebartel), ZentralBlatt

Referenced by:

§10.21(x).

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The asymptotic nature of zeros of cross-product Bessel functions. Quart. J. Mech. Appl. Math. 19 (4), pp. 511–522.

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ISSN 0033-5614, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(x).

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

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Product formulas and convolutions for angular and radial spheroidal wave functions. Trans. Amer. Math. Soc. 338 (2), pp. 695–710.

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ISSN 0002-9947, FullText, MathReview (Jean-Claude Lucquiaud), ZentralBlatt

Referenced by:

§30.10, §30.11(vi).

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12: Bibliography

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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.

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External Links:

MathReview (E. Weber), ZentralBlatt

Referenced by:

§33.9(ii).

Encodings:

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Integrals of products of Airy functions. J. Phys. A 10 (4), pp. 485–490.

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External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

(9.11.10), (9.11.5), (9.11.6), (9.11.7), (9.11.8), (9.11.9), §9.11(iv), §9.11(iv).

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Computation of modified Bessel functions and their ratios. Math. Comp. 28 (125), pp. 239–251.

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ISSN 0025-5718, FullText, MathReview (L. Lorch), ZentralBlatt

Referenced by:

§10.74(v).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

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An integral of products of ultraspherical functions and a $q$-extension. J. London Math. Soc. (2) 33 (1), pp. 133–148.

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ISSN 0024-6107, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§10.22(iv), §14.30(ii).

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13: Bibliography W

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Reduction formulae for products of theta functions. J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.

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External Links:

Document

Referenced by:

(20.7.34), §20.7(ix).

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

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Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§10.22(vi), §10.23(iv), §10.43(vi).

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Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.

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Notes:

Includes Algol code, maximum accuracy 8S.

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ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

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The asymptotic expansion of the generalized Bessel function. Proc. London Math. Soc. (2) 38, pp. 257–270.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.46.

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14: Bibliography K

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The computation of the sums of negative even powers of roots of Bessel functions. Doklady Akad. Nauk SSSR (N.S.) 77, pp. 561–564.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§10.21(xiii).

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Calculation of modified Bessel functions in a complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.

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Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 24(3), pp. 15–24

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ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.42, §10.74(iv).

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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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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

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Bessel Functions and their Applications. Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.

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Notes:

Translated from the Russian by E. V. Pankratiev

External Links:

ISBN 0-415-28130-X, MathReview (L. Debnath), ZentralBlatt

Referenced by:

§10.73(i), §10.73(i), §10.73(i).

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15: 3.8 Nonlinear Equations

… ►For the computation of zeros of Bessel functions, Coulomb functions, and conical functions as eigenvalues of finite parts of infinite tridiagonal matrices, see Grad and Zakrajšek (1973), Ikebe (1975), Ikebe et al. (1991), Ball (2000), and Gil et al. (2007a, pp. 205–213). … ►After a zero $\zeta$ has been computed, the factor $z-\zeta$ is factored out of $p(z)$ as a by-product of Horner’s scheme (§1.11(i)) for the computation of $p(\zeta )$. … ►

§3.8(v) Zeros of Analytic Functions

… ►Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. …