asymptotic expansions for large order
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11: 10.40 Asymptotic Expansions for Large Argument
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-Derivative
… ►§10.40(ii) Error Bounds for Real Argument and Order
… ►§10.40(iii) Error Bounds for Complex Argument and Order
…12: Bibliography O
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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order.
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
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Some new asymptotic expansions for Bessel functions of large orders.
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
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The asymptotic expansion of Bessel functions of large order.
Philos. Trans. Roy. Soc. London. Ser. A. 247, pp. 328–368.
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Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders.
J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
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13: 10.21 Zeros
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§10.21(vii) Asymptotic Expansions for Large Order
… ►§10.21(viii) Uniform Asymptotic Approximations for Large Order
…14: 14.26 Uniform Asymptotic Expansions
§14.26 Uniform Asymptotic Expansions
…15: Bibliography H
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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order.
Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
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16: 10.17 Asymptotic Expansions for Large Argument
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§10.17(iii) Error Bounds for Real Argument and Order
…17: Bibliography L
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Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
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18: Bibliography D
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Uniform asymptotic expansions for associated Legendre functions of large order.
Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
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19: 10.72 Mathematical Applications
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►In regions in which (10.72.1) has a simple turning point , that is, and are analytic (or with weaker conditions if is a real variable) and is a simple zero of , asymptotic expansions of the solutions for large
can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order
(§9.6(i)).
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►In regions in which the function has a simple pole at and is analytic at (the case in §10.72(i)), asymptotic expansions of the solutions of (10.72.1) for large
can be constructed in terms of Bessel functions and modified Bessel functions of order
, where is the limiting value of as .
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