zeros of Bessel functions

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11: Bibliography L

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Inequalities and approximations for zeros of Bessel functions of small order. SIAM J. Math. Anal. 14 (2), pp. 383–388.

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ISSN 0036-1410, Document, MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

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Monotonicity and convexity properties of zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 171–178.

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ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.21(iv).

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Monotonic sequences related to zeros of Bessel functions. Numer. Algorithms 49 (1-4), pp. 221–233.

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ISSN 1017-1398, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§10.21(iv), §10.21(iv).

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Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

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ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

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Some inequalities for the first positive zeros of Bessel functions. SIAM J. Math. Anal. 24 (3), pp. 814–823.

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ISSN 0036-1410, Document, MathReview (R. K. Saxena), ZentralBlatt

Referenced by:

§10.21(iv).

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12: Bibliography E

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Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comput. Appl. Math. 133 (1-2), pp. 65–83.

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ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.21(iv).

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Interlacing properties of the zeros of Bessel functions. Atti Sem. Mat. Fis. Univ. Modena XLII (2), pp. 525–529.

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ISSN 0041-8986, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.21(i).

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An upper bound for the zeros of the derivative of Bessel functions. Rend. Circ. Mat. Palermo (2) 46 (1), pp. 123–130.

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ISSN 0009-725X, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(vii).

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13: Bibliography V

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On the localization and computation of zeros of Bessel functions. Z. Angew. Math. Mech. 77 (6), pp. 467–475.

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ISSN 0044-2267, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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The topological degree theory for the localization and computation of complex zeros of Bessel functions. Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.

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ISSN 0163-0563, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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14: Bibliography O

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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

Referenced by:

§10.21(vii).

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Bessel Functions. Part III: Zeros and Associated Values. Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.

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ISBN 0-521-06153-9, MathReview (L. Fox), ZentralBlatt

Referenced by:

§10.21(vi), §10.21(viii), §10.58, §10.74(vi), 1st item, 2nd item.

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15: 13.22 Zeros

… ►where $j_{2\mu ,r}$ is the $r$th positive zero of the Bessel function $J_{2\mu }\left(x\right)$ (§10.21(i)). …

16: Bibliography P

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Interlacing of positive real zeros of Bessel functions. J. Math. Anal. Appl. 375 (1), pp. 320–322.

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ISSN 0022-247X, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§10.21(i), §10.21(i).

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Complex zeros of the modified Bessel function $K_n(Z)$ . Math. Comp. 26 (120), pp. 949–953.

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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1st item.

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Chebyshev series approximations for the zeros of the Bessel functions. J. Comput. Phys. 53 (1), pp. 188–192.

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ISSN 0021-9991, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.76(ii).

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On the computation of zeros and turning points of Bessel functions. Bull. Soc. Math. Grèce (N.S.) 31, pp. 117–122.

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MathReview (Alan M. Cohen), ZentralBlatt

Referenced by:

§10.76(ii).

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17: 18.16 Zeros

… ►Let $j_{\alpha ,m}$ be the $m$th positive zero of the Bessel function $J_{\alpha }\left(x\right)$ (§10.21(i)). Then …

18: 13.9 Zeros

… ►When and $b>0$ let ${\varphi }_r$, $r=1,2,3,\mathrm{\dots }$, be the positive zeros of $M(a,b,x)$ arranged in increasing order of magnitude, and let $j_{b-1,r}$ be the $r$th positive zero of the Bessel function $J_{b-1}\left(x\right)$ (§10.21(i)). …

19: Bibliography K

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Calculation of the complex zeros of the modified Bessel function of the second kind and its derivatives. Zh. Vychisl. Mat. i Mat. Fiz. 24 (8), pp. 1150–1163.

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Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 24(4), pp. 115–123

External Links:

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

Referenced by:

§10.42, §10.74(vi), 3rd item.

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Evaluation of complex zeros of Bessel functions $J_{\nu }(z)$ and $I_{\nu }(z)$ and their derivatives. Zh. Vychisl. Mat. i Mat. Fiz. 24 (10), pp. 1497–1513.

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Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 24(5), pp. 131–141

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

Referenced by:

§10.21(ix), §10.74(vi), 4th item.

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Calculation of the complex zeros of a Bessel function of the second kind and its derivatives. Zh. Vychisl. Mat. i Mat. Fiz. 25 (10), pp. 1457–1473, 1581 (Russian).

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Notes:

In Russian. English translation: USSR Comput. Math. Math. Phys., 25(1985), no. 5, pp. 117–128.

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ISSN 0044-4669, Document, MathReview (Jiří Hřebíček), ZentralBlatt

Referenced by:

§10.21(i), §10.21(ix), §10.74(vi), 3rd item.

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Multiple complex zeros of derivatives of the cylindrical Bessel functions. Dokl. Akad. Nauk SSSR 299 (3), pp. 614–618 (Russian).

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Notes:

In Russian. English translation: Soviet Phys. Dokl. 33(3),196–198, (1988).

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ISSN 0002-3264, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(ix), §10.74(vi).

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ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Comput. Phys. Comm. 113 (2-3), pp. 220–238.

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Notes:

Double-precision Fortran, maximum accuracy 25S.

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ISSN 0010-4655, Document, Code, ZentralBlatt

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2nd item.

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20: Bibliography M

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Zeros of Bessel functions $J_{\nu }(x)$ and $Y_{\nu }(x)$ accurate to twenty-nine significant digits. Technology Reports of the Osaka University 16 (685), pp. 1–44.

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6th item.

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On the zeros of cross-product Bessel functions. J. Math. Mech. 16, pp. 447–452.

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MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(x).

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Inequalities for the zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 166–170.

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ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.21(iv).

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On the zeros of a cross-product of Bessel functions of different orders. Z. Angew. Math. Mech. 59 (6), pp. 272–273.

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ISSN 0044-2267, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(x).

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The variation with respect to order of zeros of Bessel functions. Rend. Sem. Mat. Univ. Politec. Torino 39 (2), pp. 15–25.

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External Links:

MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

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