cross-products of Bessel functions and modified Bessel functions
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1: 10.28 Wronskians and Cross-Products
§10.28 Wronskians and Cross-Products
…2: 28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions
§28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions
… ►For further power series of Mathieu radial functions of integer order for small parameters and improved convergence rate see Larsen et al. (2009).3: 10.50 Wronskians and Cross-Products
§10.50 Wronskians and Cross-Products
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10.50.4
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►Results corresponding to (10.50.3) and (10.50.4) for and are obtainable via (10.47.12).
4: 10.6 Recurrence Relations and Derivatives
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§10.6(i) Recurrence Relations
►With defined as in §10.2(ii), … ►For results on modified quotients of the form see Onoe (1955) and Onoe (1956). ►§10.6(ii) Derivatives
… ►§10.6(iii) Cross-Products
…5: Bibliography C
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Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics.
IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
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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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The analyticity of cross-product Bessel function zeros.
Proc. Cambridge Philos. Soc. 62, pp. 215–226.
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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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6: Bibliography G
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Inequalities for modified Bessel functions and their integrals.
J. Math. Anal. Appl. 420 (1), pp. 373–386.
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On the computation of modified Bessel function ratios.
Math. Comp. 32 (143), pp. 865–875.
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Recurrence relations for cross-products of Bessel functions.
Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
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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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GNU Scientific Library
The GNU Project.
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7: 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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A code to evaluate modified Bessel functions based on the continued fraction method.
Comput. Phys. Comm. 105 (2-3), pp. 263–272.
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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities.
J. Math. Anal. Appl. 374 (2), pp. 516–528.
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8: Bibliography M
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Maplesoft.
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On the zeros of cross-product Bessel functions.
J. Math. Mech. 16, pp. 447–452.
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The MathWorks, Inc..
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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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9: 10.21 Zeros
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