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expansions in series of Bessel functions

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1: 12.18 Methods of Computation
These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …
2: 30.10 Series and Integrals
3: 10.66 Expansions in Series of Bessel Functions
§10.66 Expansions in Series of Bessel Functions
4: 13.24 Series
§13.24(ii) Expansions in Series of Bessel Functions
5: 8.7 Series Expansions
§8.7 Series Expansions
8.7.6 Γ ( a , x ) = x a e - x n = 0 L n ( a ) ( x ) n + 1 , x > 0 .
For an expansion for γ ( a , i x ) in series of Bessel functions J n ( x ) that converges rapidly when a > 0 and x ( 0 ) is small or moderate in magnitude see Barakat (1961).
6: 28.23 Expansions in Series of Bessel Functions
§28.23 Expansions in Series of Bessel Functions
7: 10.23 Sums
§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).
8: 13.11 Series
( n + 1 ) A n + 1 = ( n + b - 1 ) A n - 1 + ( 2 a - b ) A n - 2 , n = 2 , 3 , 4 , .
9: 33.9 Expansions in Series of Bessel Functions
§33.9 Expansions in Series of Bessel Functions
10: 6.10 Other Series Expansions
§6.10(ii) Expansions in Series of Spherical Bessel Functions