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asymptotic formula


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1: 36.15 Methods of Computation
Far from the bifurcation set, the leading-order asymptotic formulas of §36.11 reproduce accurately the form of the function, including the geometry of the zeros described in §36.7. …
2: 27.12 Asymptotic Formulas: Primes
§27.12 Asymptotic Formulas: Primes
3: 18.24 Hahn Class: Asymptotic Approximations
When the parameters α and β are fixed and the ratio n / N = c is a constant in the interval(0,1), uniform asymptotic formulas (as n ) of the Hahn polynomials Q n ( z ; α , β , N ) can be found in Lin and Wong (2013) for z in three overlapping regions, which together cover the entire complex plane. In particular, asymptotic formulas in terms of elementary functions are given when z = x is real and fixed. …
4: 27.11 Asymptotic Formulas: Partial Sums
§27.11 Asymptotic Formulas: Partial Sums
It is more fruitful to study partial sums and seek asymptotic formulas of the form … Equations (27.11.3)–(27.11.11) list further asymptotic formulas related to some of the functions listed in §27.2. …
5: Bibliography N
  • D. Naylor (1984) On simplified asymptotic formulas for a class of Mathieu functions. SIAM J. Math. Anal. 15 (6), pp. 1205–1213.
  • D. Naylor (1987) On a simplified asymptotic formula for the Mathieu function of the third kind. SIAM J. Math. Anal. 18 (6), pp. 1616–1629.
  • 6: Bibliography J
  • X.-S. Jin and R. Wong (1999) Asymptotic formulas for the zeros of the Meixner polynomials. J. Approx. Theory 96 (2), pp. 281–300.
  • 7: 27.14 Unrestricted Partitions
    §27.14(iii) Asymptotic Formulas
    8: 36.7 Zeros
    More general asymptotic formulas are given in Kaminski and Paris (1999). …
    9: Bibliography P
  • V. I. Pagurova (1965) An asymptotic formula for the incomplete gamma function. Ž. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).
  • 10: 2.10 Sums and Sequences
    §2.10(i) Euler–Maclaurin Formula
    Another version is the Abel–Plana formula: …
  • (c)

    The first infinite integral in (2.10.2) converges.