About the Project

approximations for large parameters

AdvancedHelp

(0.001 seconds)

1—10 of 52 matching pages

1: 34.8 Approximations for Large Parameters
§34.8 Approximations for Large Parameters
2: 13.8 Asymptotic Approximations for Large Parameters
§13.8 Asymptotic Approximations for Large Parameters
§13.8(ii) Large b and z , Fixed a and b / z
§13.8(iii) Large a
§13.8(iv) Large a and b
3: 28.26 Asymptotic Approximations for Large q
§28.26 Asymptotic Approximations for Large q
§28.26(ii) Uniform Approximations
4: 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
5: 13.20 Uniform Asymptotic Approximations for Large μ
§13.20(i) Large μ , Fixed κ
6: 13.21 Uniform Asymptotic Approximations for Large κ
§13.21 Uniform Asymptotic Approximations for Large κ
7: Bibliography O
  • 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.
  • 8: 8.12 Uniform Asymptotic Expansions for Large Parameter
    §8.12 Uniform Asymptotic Expansions for Large Parameter
    Inverse Function
    9: 2.4 Contour Integrals
    Then …
    §2.4(v) Coalescing Saddle Points: Chester, Friedman, and Ursell’s Method
    in which z is a large real or complex parameter, p ( α , t ) and q ( α , t ) are analytic functions of t and continuous in t and a second parameter α . … For large | z | , I ( α , z ) is approximated uniformly by the integral that corresponds to (2.4.19) when f ( α , w ) is replaced by a constant. …
    §2.4(vi) Other Coalescing Critical Points
    10: 2.3 Integrals of a Real Variable
    Then … Then the series obtained by substituting (2.3.7) into (2.3.1) and integrating formally term by term yields an asymptotic expansion: … (In other words, differentiation of (2.3.8) with respect to the parameter λ (or μ ) is legitimate.) … When p ( t ) is real and x is a large positive parameter, the main contribution to the integral … When the parameter x is large the contributions from the real and imaginary parts of the integrand in …