expansions in series of

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21: 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).

22: 13.11 Series

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$(n+1)A_{n+1}=(n+b-1)A_{n-1}+(2a-b)A_{n-2},$ $n=2,3,4,\mathrm{\dots }$.

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23: 8.22 Mathematical Applications

… ►See Paris and Cang (1997). …

24: 10.44 Sums

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§10.44(iii) Neumann-Type Expansions

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25: 10.23 Sums

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§10.23(iii) Series Expansions of Arbitrary Functions

… ►For other types of expansions of arbitrary functions in series of Bessel functions, see Watson (1944, Chapters 17–19) and Erdélyi et al. (1953b, §§ 7.10.2–7.10.4). … … ►For collections of sums of series involving Bessel or Hankel functions see Erdélyi et al. (1953b, §7.15), Gradshteyn and Ryzhik (2000, §§8.51–8.53), Hansen (1975), Luke (1969b, §9.4), Prudnikov et al. (1986b, pp. 651–691 and 697–700), and Wheelon (1968, pp. 48–51).

26: 6.10 Other Series Expansions

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§6.10(i) Inverse Factorial Series

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§6.10(ii) Expansions in Series of Spherical Bessel Functions

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27: 11.15 Approximations

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§11.15(i) Expansions in Chebyshev Series

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28: 5.23 Approximations

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§5.23(ii) Expansions in Chebyshev Series

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29: 7.24 Approximations

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§7.24(ii) Expansions in Chebyshev Series

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30: 28.34 Methods of Computation

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Numerical summation of the expansions in series of Bessel functions (28.24.1)–(28.24.13). These series converge quite rapidly for a wide range of values of $q$ and $z$.

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