zeros of Bessel functions

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21: Bibliography I

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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

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External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

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Computing zeros and orders of Bessel functions. J. Comput. Appl. Math. 38 (1-3), pp. 169–184.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

Encodings:

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Bounds for the small real and purely imaginary zeros of Bessel and related functions. Methods Appl. Anal. 2 (1), pp. 1–21.

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External Links:

ISSN 1073-2772, FullText, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(v).

Encodings:

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22: Bibliography C

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Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

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External Links:

ISSN 0018-9480, FullText

Referenced by:

§10.21(x).

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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).

Encodings:

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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).

Encodings:

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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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External Links:

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

Referenced by:

§10.21(x).

Encodings:

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23: Software Index

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	Open Source													With Book						Commercial
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10.77(x) Zeros of Bessel Functions					✓							a	✓	✓	✓				✓		✓	✓	a
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24: 10.23 Sums

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10.23.19 $$a_m=\frac{2}{{(J_{\nu +1}\left(j_{\nu ,m}\right))}^2}{\int }_0^{1}tf(t)J_{\nu }\left(j_{\nu ,m}t\right)dt,$$ $\nu \ge -\frac{1}{2}$,

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Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $dx$: differential of $x$ , $\int$: integral, $j_{\nu ,m}$: zeros of the Bessel function $J_{\nu }\left(x\right)$ , $m$: integer, $\nu$: complex parameter, $a_k$ and $f(t)$

Referenced by:

§10.74(vii)

Permalink:

http://dlmf.nist.gov/10.23.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §10.23(iii), §10.23(iii), §10.23 and Ch.10

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10.23.21 $$x^{\nu }=\sum _{m=1}^{\mathrm{\infty }}\frac{2J_{\nu }\left(j_{\nu ,m}x\right)}{j_{\nu ,m}{J}_{\nu +1}\left(j_{\nu ,m}\right)},$$ .

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Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $j_{\nu ,m}$: zeros of the Bessel function $J_{\nu }\left(x\right)$ , $m$: integer, $x$: real variable and $\nu$: complex parameter

Referenced by:

§10.23(iii)

Permalink:

http://dlmf.nist.gov/10.23.E21

Encodings:

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See also:

Annotations for §10.23(iii), §10.23(iii), §10.23 and Ch.10

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25: Bibliography G

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On the complex zeros of Airy and Bessel functions and those of their derivatives. Anal. Appl. (Singap.) 12 (5), pp. 537–561.

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External Links:

ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§9.9(i), §9.9(i).

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On the exceptional zeros of cross-products of derivatives of spherical Bessel functions. Z. Angew. Math. Phys. 36 (3), pp. 491–494.

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External Links:

ISSN 0044-2275, Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§10.58.

Encodings:

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Method for evaluation of zeros of Bessel functions. J. Inst. Math. Appl. 11, pp. 57–72.

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External Links:

ISSN 0020-2932, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

Encodings:

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26: Bibliography S

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A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.

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External Links:

Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§10.21(x).

Encodings:

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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.

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External Links:

ISSN 0025-5718, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

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On the calculation of complex zeros of the modified Bessel function of the second kind. Dokl. Akad. Nauk SSSR 280 (2), pp. 296–299.

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Notes:

English translation in Soviet Math. Dokl. 31(1), pp. 78–81

External Links:

ISSN 0002-3264, MathReview (I. F. Kushnirchuk), ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

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27: 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). …

28: Bibliography T

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An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives. J. Comput. Phys. 32 (2), pp. 270–279.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.74(vi), §10.77(x).

Encodings:

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29: Bibliography B

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Automatic computation of zeros of Bessel functions and other special functions. SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.

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External Links:

ISSN 1064-8275, Document, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.74(vi), §3.8(iii).

Encodings:

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Concerning the zeros of some functions related to Bessel functions. J. Mathematical Phys. 10 (9), pp. 1729–1744.

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External Links:

Document, MathReview (C. V. Coffman), ZentralBlatt

Referenced by:

§10.21(xi).

Encodings:

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Bessel Functions. Part I: Functions of Orders Zero and Unity. Mathematical Tables, Volume 6, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-04319-0, ZentralBlatt

Referenced by:

§10.1, 1st item, 1st item, 1st item.

Encodings:

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30: 10.24 Functions of Imaginary Order

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