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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: 10.19 Asymptotic Expansions for Large Order
§10.19 Asymptotic Expansions for Large Order
§10.19(i) Asymptotic Forms
§10.19(ii) Debye’s Expansions
§10.19(iii) Transition Region
See also §10.20(i).
4: 10.41 Asymptotic Expansions for Large Order
§10.41 Asymptotic Expansions for Large Order
§10.41(i) Asymptotic Forms
§10.41(v) Double Asymptotic Properties (Continued)
5: 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(iii) Double Asymptotic Properties
For asymptotic properties of the expansions (10.20.4)–(10.20.6) with respect to large values of z see §10.41(v).
6: 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).
7: 11.6 Asymptotic Expansions
§11.6(ii) Large | ν | , Fixed z
8: 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). …
9: 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). …
10: 11.11 Asymptotic Expansions of Anger–Weber Functions
§11.11(ii) Large | ν | , Fixed z