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Bessel-function expansion

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11: 13.24 Series
§13.24(ii) Expansions in Series of Bessel Functions
Additional expansions in terms of Bessel functions are given in Luke (1959). …
12: 26.10 Integer Partitions: Other Restrictions
§26.10(vi) Bessel-Function Expansion
13: 11.13 Methods of Computation
Although the power-series expansions (11.2.1) and (11.2.2), and the Bessel-function expansions of §11.4(iv) converge for all finite values of z , they are cumbersome to use when | z | is large owing to slowness of convergence and cancellation. …
14: 10.66 Expansions in Series of Bessel Functions
§10.66 Expansions in Series of Bessel Functions
15: 10.17 Asymptotic Expansions for Large Argument
§10.17 Asymptotic Expansions for Large Argument
§10.17(ii) Asymptotic Expansions of Derivatives
§10.17(iii) Error Bounds for Real Argument and Order
§10.17(v) Exponentially-Improved Expansions
For higher re-expansions of the remainder terms see Olde Daalhuis and Olver (1995a) and Olde Daalhuis (1995, 1996).
16: 33.9 Expansions in Series of Bessel Functions
§33.9 Expansions in Series of Bessel Functions
§33.9(i) Spherical Bessel Functions
§33.9(ii) Bessel Functions and Modified Bessel Functions
17: 30.10 Series and Integrals
For expansions in products of spherical Bessel functions, see Flammer (1957, Chapter 6).
18: 10.20 Uniform Asymptotic Expansions for Large Order
§10.20 Uniform Asymptotic Expansions for Large Order
10.20.5 Y ν ( ν z ) ( 4 ζ 1 z 2 ) 1 4 ( Bi ( ν 2 3 ζ ) ν 1 3 k = 0 A k ( ζ ) ν 2 k + Bi ( ν 2 3 ζ ) ν 5 3 k = 0 B k ( ζ ) ν 2 k ) ,
§10.20(iii) Double Asymptotic Properties
For asymptotic properties of the expansions (10.20.4)–(10.20.6) with respect to large values of z see §10.41(v).
19: 11.9 Lommel Functions
§11.9(ii) Expansions in Series of Bessel Functions
20: 7.6 Series Expansions
§7.6(ii) Expansions in Series of Spherical Bessel Functions