expansions in series of spherical Bessel functions
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1: 30.10 Series and Integrals
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2: 6.10 Other Series Expansions
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§6.10(ii) Expansions in Series of Spherical Bessel Functions
…3: 8.7 Series Expansions
§8.7 Series Expansions
…4: 7.6 Series Expansions
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§7.6(ii) Expansions in Series of Spherical Bessel Functions
…5: 8.21 Generalized Sine and Cosine Integrals
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Spherical-Bessel-Function Expansions
…6: 6.18 Methods of Computation
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►For small or moderate values of and , the expansion in power series (§6.6) or in series of spherical Bessel functions (§6.10(ii)) can be used.
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7: 33.9 Expansions in Series of Bessel Functions
§33.9 Expansions in Series of Bessel Functions
►§33.9(i) Spherical Bessel Functions
… ►where the function is as in §10.47(ii), , , and … ►§33.9(ii) Bessel Functions and Modified Bessel Functions
►In this subsection the functions , , and are as in §§10.2(ii) and 10.25(ii). …8: 10.74 Methods of Computation
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►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument or is sufficiently small in absolute value.
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►In the case of the spherical Bessel functions the explicit formulas given in §§10.49(i) and 10.49(ii) are terminating cases of the asymptotic expansions given in §§10.17(i) and 10.40(i) for the Bessel functions and modified Bessel functions.
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Fourier–Bessel Expansion
… ►Spherical Bessel Transform
…9: 14.15 Uniform Asymptotic Approximations
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►In other words, the convergent hypergeometric series expansions of are also generalized (and uniform) asymptotic expansions as , with scale , ; compare §2.1(v).
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►Here and are the modified Bessel functions (§10.25(ii)).
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►For the Bessel functions
and see §10.2(ii), and for the
functions associated with and see §2.8(iv).
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►For convergent series expansions see Dunster (2004).
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►See also Olver (1997b, pp. 311–313) and §18.15(iii) for a generalized asymptotic expansion in terms of elementary functions for Legendre polynomials as with fixed.
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10: Bibliography V
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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An infinite series of Weber’s parabolic cylinder functions.
Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
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Some novel infinite series of spherical Bessel functions.
Quart. Appl. Math. 42 (3), pp. 321–324.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Fourier series representation of Ferrers function
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