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asymptotic expansions for large argument

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1: 13.19 Asymptotic Expansions for Large Argument
§13.19 Asymptotic Expansions for Large Argument
2: 10.17 Asymptotic Expansions for Large Argument
§10.17 Asymptotic Expansions for Large Argument
§10.17(ii) Asymptotic Expansions of Derivatives
§10.17(iii) Error Bounds for Real Argument and Order
§10.17(v) Exponentially-Improved Expansions
For higher re-expansions of the remainder terms see Olde Daalhuis and Olver (1995a) and Olde Daalhuis (1995, 1996).
3: 13.7 Asymptotic Expansions for Large Argument
§13.7 Asymptotic Expansions for Large Argument
§13.7(ii) Error Bounds
§13.7(iii) Exponentially-Improved Expansion
For extensions to hyperasymptotic expansions see Olde Daalhuis and Olver (1995a).
4: 10.40 Asymptotic Expansions for Large Argument
§10.40 Asymptotic Expansions for Large Argument
Products
§10.40(ii) Error Bounds for Real Argument and Order
§10.40(iv) Exponentially-Improved Expansions
5: 10.67 Asymptotic Expansions for Large Argument
§10.67 Asymptotic Expansions for Large Argument
§10.67(i) ber ν x , bei ν x , ker ν x , kei ν x , and Derivatives
§10.67(ii) Cross-Products and Sums of Squares in the Case ν = 0
6: Bibliography N
  • G. Nemes (2017b) Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.
  • G. Nemes (2018) Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.
  • 7: 11.11 Asymptotic Expansions of Anger–Weber Functions
    §11.11(i) Large | z | , Fixed ν
    8: 11.6 Asymptotic Expansions
    §11.6(i) Large | z | , Fixed ν
    9: 10.18 Modulus and Phase Functions
    §10.18(iii) Asymptotic Expansions for Large Argument
    The remainder after k terms in (10.18.17) does not exceed the ( k + 1 ) th term in absolute value and is of the same sign, provided that k > ν - 1 2 .
    10: 10.68 Modulus and Phase Functions
    §10.68(iii) Asymptotic Expansions for Large Argument