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11: 11.11 Asymptotic Expansions of Anger–Weber Functions
§11.11(i) Large | z | , Fixed ν
12: 11.6 Asymptotic Expansions
§11.6(i) Large | z | , Fixed ν
13: 11.9 Lommel Functions
§11.9(iii) Asymptotic Expansion
14: 2.11 Remainder Terms; Stokes Phenomenon
However, on combining (2.11.6) with the connection formula (8.19.18), with m = 1 , we derive … For large | z | , with | ph z | 3 2 π - δ ( < 3 2 π ), the Whittaker function of the second kind has the asymptotic expansion (§13.19) …
15: Bibliography W
  • J. A. Wheeler (1937) Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.
  • 16: Bibliography F
  • L. Fox (1960) Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments. National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
  • 17: 9.18 Tables
  • Miller (1946) tabulates Ai ( x ) , Ai ( x ) for x = - 20 ( .01 ) 2 ; log 10 Ai ( x ) , Ai ( x ) / Ai ( x ) for x = 0 ( .1 ) 25 ( 1 ) 75 ; Bi ( x ) , Bi ( x ) for x = - 10 ( .1 ) 2.5 ; log 10 Bi ( x ) , Bi ( x ) / Bi ( x ) for x = 0 ( .1 ) 10 ; M ( x ) , N ( x ) , θ ( x ) , ϕ ( x ) (respectively F ( x ) , G ( x ) , χ ( x ) , ψ ( x ) ) for x = - 80 ( 1 ) - 30 ( .1 ) 0 . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.

  • 18: 2.10 Sums and Sequences
    Hence …
    19: Bibliography C
  • F. Calogero (1978) Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial L n α ( x )  as the index α  and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
  • 20: Bibliography T
  • J. Todd (1954) Evaluation of the exponential integral for large complex arguments. J. Research Nat. Bur. Standards 52, pp. 313–317.