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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: 28.30 Expansions in Series of Eigenfunctions
§28.30 Expansions in Series of Eigenfunctions
4: 13.24 Series
§13.24(i) Expansions in Series of Whittaker Functions
For expansions of arbitrary functions in series of M κ , μ ( z ) functions see Schäfke (1961b).
§13.24(ii) Expansions in Series of Bessel Functions
5: 18.40 Methods of Computation
However, for applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. …
6: 28.19 Expansions in Series of me ν + 2 n Functions
§28.19 Expansions in Series of me ν + 2 n Functions
7: 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).
8: 28.11 Expansions in Series of Mathieu Functions
§28.11 Expansions in Series of Mathieu Functions
28.11.7 sin ( 2 m + 2 ) z = n = 0 B 2 m + 2 2 n + 2 ( q ) se 2 n + 2 ( z , q ) .
9: 10.66 Expansions in Series of Bessel Functions
§10.66 Expansions in Series of Bessel Functions
10: 12.20 Approximations
§12.20 Approximations