About the Project
NIST

large parameters

AdvancedHelp

(0.002 seconds)

1—10 of 91 matching pages

1: 34.8 Approximations for Large Parameters
§34.8 Approximations for Large Parameters
For large values of the parameters in the 3 j , 6 j , and 9 j symbols, different asymptotic forms are obtained depending on which parameters are large. …
2: 16.22 Asymptotic Expansions
For asymptotic expansions of Meijer G -functions with large parameters see Fields (1973, 1983).
3: Bibliography U
  • F. Ursell (1972) Integrals with a large parameter. Several nearly coincident saddle-points. Proc. Cambridge Philos. Soc. 72, pp. 49–65.
  • F. Ursell (1980) Integrals with a large parameter: A double complex integral with four nearly coincident saddle-points. Math. Proc. Cambridge Philos. Soc. 87 (2), pp. 249–273.
  • F. Ursell (1984) Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
  • 4: 13.8 Asymptotic Approximations for Large Parameters
    §13.8 Asymptotic Approximations for Large Parameters
    §13.8(i) Large | b | , Fixed a and z
    §13.8(ii) Large b and z , Fixed a and b / z
    §13.8(iii) Large a
    5: 8.18 Asymptotic Expansions of I x ( a , b )
    §8.18(i) Large Parameters, Fixed x
    §8.18(ii) Large Parameters: Uniform Asymptotic Expansions
    Symmetric Case
    General Case
    Inverse Function
    6: Bibliography O
  • A. B. Olde Daalhuis (2003a) Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.
  • A. B. Olde Daalhuis (2003b) Uniform asymptotic expansions for hypergeometric functions with large parameters. II. Analysis and Applications (Singapore) 1 (1), pp. 121–128.
  • A. B. Olde Daalhuis (2010) Uniform asymptotic expansions for hypergeometric functions with large parameters. III. Analysis and Applications (Singapore) 8 (2), pp. 199–210.
  • F. W. J. Olver (1975b) Legendre functions with both parameters large. Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
  • F. W. J. Olver (1980b) Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
  • 7: 28.8 Asymptotic Expansions for Large q
    §28.8 Asymptotic Expansions for Large q
    Barrett’s Expansions
    The approximations apply when the parameters a and q are real and large, and are uniform with respect to various regions in the z -plane. …
    Dunster’s Approximations
    8: 28.26 Asymptotic Approximations for Large q
    §28.26 Asymptotic Approximations for Large q
    §28.26(ii) Uniform Approximations
    9: 12.11 Zeros
    §12.11(iii) Asymptotic Expansions for Large Parameter
    10: 13.20 Uniform Asymptotic Approximations for Large μ
    §13.20(i) Large μ , Fixed κ