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uniform asymptotic expansions for large order

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1: 10.57 Uniform Asymptotic Expansions for Large Order
§10.57 Uniform Asymptotic Expansions for Large Order
2: 10.69 Uniform Asymptotic Expansions for Large Order
§10.69 Uniform Asymptotic Expansions for Large Order
3: 10.20 Uniform Asymptotic Expansions for Large Order
§10.20 Uniform Asymptotic Expansions for Large Order
10.20.5 Y ν ( ν z ) - ( 4 ζ 1 - z 2 ) 1 4 ( Bi ( ν 2 3 ζ ) ν 1 3 k = 0 A k ( ζ ) ν 2 k + Bi ( ν 2 3 ζ ) ν 5 3 k = 0 B k ( ζ ) ν 2 k ) ,
10.20.9 H ν ( 1 ) ( ν z ) H ν ( 2 ) ( ν z ) } 4 e 2 π i / 3 z ( 1 - z 2 4 ζ ) 1 4 ( e 2 π i / 3 Ai ( e ± 2 π i / 3 ν 2 3 ζ ) ν 4 3 k = 0 C k ( ζ ) ν 2 k + Ai ( e ± 2 π i / 3 ν 2 3 ζ ) ν 2 3 k = 0 D k ( ζ ) ν 2 k ) ,
For asymptotic properties of the expansions (10.20.4)–(10.20.6) with respect to large values of z see §10.41(v).
4: 10.1 Special Notation
For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
5: 10.41 Asymptotic Expansions for Large Order
§10.41(ii) Uniform Expansions for Real Variable
6: 10.24 Functions of Imaginary Order
For mathematical properties and applications of J ~ ν ( x ) and Y ~ ν ( x ) , including zeros and uniform asymptotic expansions for large ν , see Dunster (1990a). …
7: 10.45 Functions of Imaginary Order
For properties of I ~ ν ( x ) and K ~ ν ( x ) , including uniform asymptotic expansions for large ν and zeros, see Dunster (1990a). …
8: 14.26 Uniform Asymptotic Expansions
§14.26 Uniform Asymptotic Expansions
9: 10.21 Zeros
§10.21(vii) Asymptotic Expansions for Large Order
§10.21(viii) Uniform Asymptotic Approximations for Large Order
10: Bibliography O
  • F. W. J. Olver (1959) Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders. J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.