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11: Bibliography H
  • B. A. Hargrave and B. D. Sleeman (1977) Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.
  • C. J. Howls and A. B. Olde Daalhuis (1999) 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.
  • 12: 10.45 Functions of Imaginary Order
    In consequence of (10.45.5)–(10.45.7), I ~ ν ( x ) and K ~ ν ( x ) comprise a numerically satisfactory pair of solutions of (10.45.1) when x is large, and either I ~ ν ( x ) and ( 1 / π ) sinh ( π ν ) K ~ ν ( x ) , or I ~ ν ( x ) and K ~ ν ( x ) , comprise a numerically satisfactory pair when x is small, depending whether ν 0 or ν = 0 . … For properties of I ~ ν ( x ) and K ~ ν ( x ) , including uniform asymptotic expansions for large ν and zeros, see Dunster (1990a). …
    13: 14.15 Uniform Asymptotic Approximations
    §14.15(i) Large μ , Fixed ν
    For asymptotic expansions and explicit error bounds, see Dunster (2003b). …
    14: Bibliography J
  • D. S. Jones (2006) Parabolic cylinder functions of large order. J. Comput. Appl. Math. 190 (1-2), pp. 453–469.
  • 15: 11.6 Asymptotic Expansions
    §11.6(ii) Large | ν | , Fixed z
    16: Bibliography P
  • R. B. Paris (2004) Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
  • 17: 10.21 Zeros
    §10.21(vii) Asymptotic Expansions for Large Order
    §10.21(viii) Uniform Asymptotic Approximations for Large Order
    18: 11.11 Asymptotic Expansions of Anger–Weber Functions
    §11.11(ii) Large | ν | , Fixed z
    19: Bibliography D
  • T. M. Dunster (1990a) Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21 (4), pp. 995–1018.
  • T. M. Dunster (2003b) Uniform asymptotic expansions for associated Legendre functions of large order. Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
  • 20: Bibliography L
  • J. L. López (1999) Asymptotic expansions of the Whittaker functions for large order parameter. Methods Appl. Anal. 6 (2), pp. 249–256.