Watson expansions
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11: 8.21 Generalized Sine and Cosine Integrals
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§8.21(vi) Series Expansions
►Power-Series Expansions
… ►Spherical-Bessel-Function Expansions
… ►For (8.21.16), (8.21.17), and further expansions in series of Bessel functions see Luke (1969b, pp. 56–57). … ►§8.21(viii) Asymptotic Expansions
…12: 22.11 Fourier and Hyperbolic Series
§22.11 Fourier and Hyperbolic Series
… ►Similar expansions for and follow immediately from (22.6.1). … ►Again, similar expansions for and may be derived via (22.6.1). …13: Bibliography S
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Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma.
SIAM J. Math. Anal. 16 (4), pp. 896–906.
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14: 10.17 Asymptotic Expansions for Large Argument
§10.17 Asymptotic Expansions for Large Argument
►§10.17(i) Hankel’s Expansions
… ► ►§10.17(ii) Asymptotic Expansions of Derivatives
… ►§10.17(v) Exponentially-Improved Expansions
…15: 10.19 Asymptotic Expansions for Large Order
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►For higher coefficients in (10.19.8) in the case (that is, in the expansions of and ), see Watson (1944, §8.21), Temme (1997), and Jentschura and Lötstedt (2012).
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16: 10.23 Sums
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►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).
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17: 10.12 Generating Function and Associated Series
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►Jacobi–Anger expansions: for ,
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18: 10.44 Sums
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►For results analogous to (10.23.7) and (10.23.8) see Watson (1944, §§11.3 and 11.41).
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§10.44(iii) Neumann-Type Expansions
…19: 10.21 Zeros
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►No two of the functions , , , have any common zeros other than ; see Watson (1944, §15.28).
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