expansions in series of
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1: 12.18 Methods of Computation
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►These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions.
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2: 30.10 Series and Integrals
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3: 28.30 Expansions in Series of Eigenfunctions
§28.30 Expansions in Series of Eigenfunctions
…4: 13.24 Series
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§13.24(i) Expansions in Series of Whittaker Functions
►For expansions of arbitrary functions in series of functions see Schäfke (1961b). ►§13.24(ii) Expansions in Series of Bessel Functions
…5: 18.40 Methods of Computation
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►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.
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6: 28.19 Expansions in Series of Functions
§28.19 Expansions in Series of Functions
…7: 8.7 Series Expansions
§8.7 Series Expansions
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8.7.6
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►For an expansion for
in series of Bessel functions that converges rapidly when and () is small or moderate in magnitude see Barakat (1961).