asymptotic approximation

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41—50 of 133 matching pages

41: 9.16 Physical Applications

… ►Again, the quest for asymptotic approximations that are uniformly valid solutions to this equation in the neighborhoods of critical points leads (after choosing solvable equations with similar asymptotic properties) to Airy functions. … ►This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point. …

42: 18.32 OP’s with Respect to Freud Weights

… ►However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986). … ►For asymptotic approximations to OP’s that correspond to Freud weights with more general functions

Q(x)

see Deift et al. (1999a, b), Bleher and Its (1999), and Kriecherbauer and McLaughlin (1999). …

43: 14.15 Uniform Asymptotic Approximations

§14.15 Uniform Asymptotic Approximations

►

§14.15(i) Large $\mu$ , Fixed $\nu$

… ►For asymptotic expansions and explicit error bounds, see Dunster (2003b). ►

§14.15(iii) Large $\nu$ , Fixed $\mu$

… ►

44: 29.20 Methods of Computation

… ►Initial approximations to the eigenvalues can be found, for example, from the asymptotic expansions supplied in §29.7(i). … ►A fourth method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree. …

45: 8.11 Asymptotic Approximations and Expansions

§8.11 Asymptotic Approximations and Expansions

… ►where

\delta

denotes an arbitrary small positive constant. … ►

46: 28.25 Asymptotic Expansions for Large $\Re z$

§28.25 Asymptotic Expansions for Large $\Re z$

…

47: 8.13 Zeros

… ►For asymptotic approximations for

x_{+}(a)

and

x_{-}(a)

a\to-\infty

see Tricomi (1950b), with corrections by Kölbig (1972b). For more accurate asymptotic approximations see Thompson (2012). …

48: 19.27 Asymptotic Approximations and Expansions

§19.27 Asymptotic Approximations and Expansions

… ►Although they are obtained (with some exceptions) by approximating uniformly the integrand of each elliptic integral, some occur also as the leading terms of known asymptotic series with error bounds (Wong (1983, §4), Carlson and Gustafson (1985), López (2000, 2001)). … ►

49: 13.20 Uniform Asymptotic Approximations for Large $\mu$

§13.20 Uniform Asymptotic Approximations for Large $\mu$

►

§13.20(i) Large $\mu$ , Fixed $\kappa$

… ► … ►

50: 35.5 Bessel Functions of Matrix Argument

… ►

§35.5(iii) Asymptotic Approximations

►For asymptotic approximations for Bessel functions of matrix argument, see Herz (1955) and Butler and Wood (2003).